A002824 -id:A002824 - cp's OEIS frontend

A259336 Erroneous version of A002824.

Original entry on oeis.org

1, 3, 18, 190, 3375, 93681

Offset: 2

N. J. A. Sloane, Jun 02 2017

dead

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

A001035 Number of partially ordered sets ("posets") with n labeled elements (or labeled acyclic transitive digraphs).

Original entry on oeis.org

1, 1, 3, 19, 219, 4231, 130023, 6129859, 431723379, 44511042511, 6611065248783, 1396281677105899, 414864951055853499, 171850728381587059351, 98484324257128207032183, 77567171020440688353049939, 83480529785490157813844256579, 122152541250295322862941281269151, 241939392597201176602897820148085023

Offset: 0

N. J. A. Sloane

From Altug Alkan, Dec 22 2015: (Start)
a(p^k) == 1 (mod p) and a(n + p) == a(n + 1) (mod p) for all primes p.
a(0+19) == a(0+1) (mod 19) or a(19^1) == 1 (mod 19), that is, a(19) mod 19 = 1.
a(2+17) == a(2+1) (mod 17). So a(19) == 19 (mod 17), that is, a(19) mod 17 = 2.
a(6+13) == a(6+1) (mod 13). So a(19) == 6129859 (mod 13), that is, a(19) mod 13 = 8.
a(8+11) == a(8+1) (mod 11). So a(19) == 44511042511 (mod 11), that is, a(19) mod 11 = 1.
a(12+7) == a(12+1) (mod 7). So a(19) == 171850728381587059351 (mod 7), that is, a(19) mod 7 = 1.
a(14+5) == a(14+1) (mod 5). So a(19) == 77567171020440688353049939 (mod 5), that is, a(19) mod 5 = 4.
a(16+3) == a(16+1) (mod 3). So a(19) == 122152541250295322862941281269151 (mod 3), that is, a(19) mod 3 = 1.
a(17+2) == a(17+1) (mod 2). So a(19) mod 2 = 1.
In conclusion, a(19) is a number of the form 2*3*5*7*11*13*17*19*n - 1615151, that is, 9699690*n - 1615151.
Additionally, for n > 0, note that the last digit of a(n) has the simple periodic pattern: 1,3,9,9,1,3,9,9,1,3,9,9,...
(End)
Number of rank n sublattices of the Boolean algebra B_n. - Kevin Long, Nov 20 2018
a(n) is the number of n X n idempotent Boolean relation matrices (A121337) that have rank n. - Geoffrey Critzer, Aug 16 2023
a(19) == 163279579 (mod 232792560). - Didier Garcia, Feb 06 2025

			R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, page 98, Fig. 3-1 shows the unlabeled posets with <= 4 points.
From _Gus Wiseman_, Aug 14 2019: (Start)
Also the number of T_0 topologies with n points. For example, the a(0) = 1 through a(3) = 19 topologies are:
  {}  {}{1}  {}{1}{12}     {}{1}{12}{123}
             {}{2}{12}     {}{1}{13}{123}
             {}{1}{2}{12}  {}{2}{12}{123}
                           {}{2}{23}{123}
                           {}{3}{13}{123}
                           {}{3}{23}{123}
                           {}{1}{2}{12}{123}
                           {}{1}{3}{13}{123}
                           {}{2}{3}{23}{123}
                           {}{1}{12}{13}{123}
                           {}{2}{12}{23}{123}
                           {}{3}{13}{23}{123}
                           {}{1}{2}{12}{13}{123}
                           {}{1}{2}{12}{23}{123}
                           {}{1}{3}{12}{13}{123}
                           {}{1}{3}{13}{23}{123}
                           {}{2}{3}{12}{23}{123}
                           {}{2}{3}{13}{23}{123}
                           {}{1}{2}{3}{12}{13}{23}{123}
(End)

G. Birkhoff, Lattice Theory, Amer. Math. Soc., 1961, p. 4.
Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 427.
K. K.-H. Butler, A Moore-Penrose inverse for Boolean relation matrices, pp. 18-28 of Combinatorial Mathematics (Proceedings 2nd Australian Conf.), Lect. Notes Math. 403, 1974.
K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
K. K. H. Butler and G. Markowsky. "The number of partially ordered sets. I." Journal of Korean Mathematical Society 11.1 (1974).
S. D. Chatterji, The number of topologies on n points, Manuscript, 1966.
L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 60, 229.
M. Erné, Struktur- und Anzahlformeln für Topologien auf endlichen Mengen, PhD dissertation, Westfälische Wilhelms-Universität zu Münster, 1972.
M. Erné and K. Stege, The number of labeled orders on fifteen elements, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, pages 96ff; Vol. 2, Problem 5.39, p. 88.

Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); arXiv preprint, arXiv:2312.07716 [math.CO], 2023.
Juliana Bowles and Marco B. Caminati, A Verified Algorithm Enumerating Event Structures, arXiv:1705.07228 [cs.LO], 2017.
G. Brinkmann and B. D. McKay, Posets on up to 16 Points, Order 19 (2) (2002) 147-179.
J. I. Brown and S. Watson, The number of complements of a topology on n points is at least 2^n (except for some special cases), Discr. Math., 154 (1996), 27-39.
K. K.-H. Butler, The number of partially ordered sets, Journal of Combinatorial Theory, Series B 13.3 (1972): 276-289.
K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184. [Annotated scan of pages 180 and 183 only]
K. K.-H. Butler and G. Markowsky, The number of partially ordered sets. II., J. Korean Math. Soc 11 (1974): 7-17.
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
S. D. Chatterji, The number of topologies on n points, Manuscript, 1966. [Annotated scanned copy]
Narendrakumar R. Dasre and Pritam Gujarathi, Approximating the Bounds for Number of Partially Ordered Sets with n Labeled Elements, Computing in Engineering and Technology, Advances in Intelligent Systems and Computing, Vol. 1025, Springer (Singapore 2019), 349-356.
M. Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259.
M. Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259. (Annotated scanned copy)
M. Erné and K. Stege, The number of partially ordered (labeled) sets, Preprint, 1989. (Annotated scanned copy)
M. Erné and K. Stege, Counting Finite Posets and Topologies, Order, 8 (1991), 247-265.
J. W. Evans, F. Harary and M. S. Lynn, On the computer enumeration of finite topologies, Commun. ACM, 10 (1967), 295-297, 313.
J. W. Evans, F. Harary and M. S. Lynn, On the computer enumeration of finite topologies, Commun. ACM, 10 (1967), 295-297, 313. [Annotated scanned copy]
S. R. Finch, Transitive relations, topologies and partial orders.
S. R. Finch, Transitive relations, topologies and partialorders, June 5, 2003. [Cached copy, with permission of the author]
Eldar Fischer, Johann A. Makowsky, and Vsevolod Rakita, MC-finiteness of restricted set partition functions, arXiv:2302.08265 [math.CO], 2023.
Didier Garcia, Proof of a(19) formula [in French].
Didier Garcia, Two conjectures concerning a(n) [in French].
Joël Gay and Vincent Pilaud, The weak order on Weyl posets, arXiv:1804.06572 [math.CO], 2018.
G. Grekos, Letter to N. J. A. Sloane, Oct 31 1994, with attachments.
J. Heitzig and J. Reinhold, The number of unlabeled orders on fourteen elements, Order 17 (2000) no. 4, 333-341.
Richard Kenyon, Maxim Kontsevich, Oleg Ogievetsky, Cosmin Pohoata, Will Sawin, and Senya Shlosman, The miracle of integer eigenvalues, arXiv:2401.05291 [math.CO], 2024. See p. 4.
Dongseok Kim, Young Soo Kwon, and Jaeun Lee, Enumerations of finite topologies associated with a finite graph, arXiv preprint arXiv:1206.0550 [math.CO], 2012. - From _N. J. A. Sloane_, Nov 09 2012
M. Y. Kizmaz, On The Number Of Topologies On A Finite Set, arXiv preprint arXiv:1503.08359 [math.NT], 2015.
D. J. Kleitman and B. L. Rothschild, Asymptotic enumeration of partial orders on a finite set, Trans. Amer. Math. Soc., 205 (1975) 205-220.
G. Kreweras, Dénombrement des ordres étagés, Discrete Math., 53 (1985), 147-149.
Institut f. Mathematik, Univ. Hanover, Erne/Heitzig/Reinhold papers.
Sami Lazaar, Houssem Sabri, and Randa Tahri, Structural and Numerical Studies of Some Topological Properties for Alexandroff Spaces, Bull. Iran. Math. Soc. (2021).
N. Lygeros and P. Zimmermann, Computation of P(14), the number of posets with 14 elements: 1.338.193.159.771.
G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
Bob Proctor, Chapel Hill Poset Atlas.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
Ivo Rosenberg and N. J. A. Sloane, Correspondence, 1971.
D. Rusin, Further information and references. [Broken link]
D. Rusin, Further information and references. [Cached copy]
A. Shafaat, On the number of topologies definable for a finite set, J. Austral. Math. Soc., 8 (1968), 194-198.
N. J. A. Sloane, List of sequences related to partial orders, circa 1972.
N. J. A. Sloane, List of sequences related to partial orders, circa 1972.
N. J. A. Sloane, Classic Sequences.
Gus Wiseman, Hasse diagrams of the a(4) = 219 posets.
J. A. Wright, There are 718 6-point topologies, quasiorderings and transgraphs, Preprint, 1970. [Annotated scanned copy]
J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences.
Index entries for sequences related to posets

Cf. A000798 (labeled topologies), A001930 (unlabeled topologies), A000112 (unlabeled posets), A006057.
Sequences in the Erné (1974) paper: A000798, A001035, A006056, A006057, A001929, A001927, A006058, A006059, A000110.
Cf. A316978, A319564, A326876, A326906, A326939, A326943, A326944, A326947.

dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
Table[Length[Select[Subsets[Subsets[Range[n]]],MemberQ[#,{}]&&MemberQ[#,Range[n]]&&UnsameQ@@dual[#]&&SubsetQ[#,Union@@@Tuples[#,2]]&&SubsetQ[#,Intersection@@@Tuples[#,2]]&]],{n,0,3}] (* Gus Wiseman, Aug 14 2019 *)

A000798(n) = Sum_{k=0..n} Stirling2(n,k)*a(k).
Related to A000112 by Erné's formulas: a(n+1) = -s(n, 1), a(n+2) = n*a(n+1) + s(n, 2), a(n+3) = binomial(n+4, 2)*a(n+2) - s(n, 3), where s(n, k) = sum(binomial(n+k-1-m, k-1)*binomial(n+k, m)*sum((m!)/(number of automorphisms of P)*(-(number of antichains of P))^k, P an unlabeled poset with m elements), m=0..n).
From Altug Alkan, Dec 22 2015: (Start)
a(p^k) == 1 (mod p) for all primes p and for all nonnegative integers k.
a(n + p) == a(n + 1) (mod p) for all primes p and for all nonnegative integers n.
If n = 1, then a(1 + p) == a(2) (mod p), that is, a(p + 1) == 3 (mod p).
If n = p, then a(p + p) == a(p + 1) (mod p), that is, a(2*p) == a(p + 1) (mod p).
In conclusion, a(2*p) == 3 (mod p) for all primes p.
(End)
a(n) = Sum_{k=0..n} Stirling1(n,k)*A000798(k). - Tian Vlasic, Feb 25 2022

a(15)-a(16) from Jobst Heitzig (heitzig(AT)math.uni-hannover.de), Jul 03 2000

a(17)-a(18) from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008

A008827 Number of proper partitions of a set of n labeled elements.

Original entry on oeis.org

0, 3, 13, 50, 201, 875, 4138, 21145, 115973, 678568, 4213595, 27644435, 190899320, 1382958543, 10480142145, 82864869802, 682076806157, 5832742205055, 51724158235370, 474869816156749, 4506715738447321, 44152005855084344, 445958869294805287, 4638590332229999351

Offset: 2

N. J. A. Sloane

nonn

Previous name: Coefficients from fractional iteration of exp(x) - 1.
From Harry Richman, Mar 18 2023: (Start)
A "proper partition" of a set is a set partition in which there is more than one part, and there is some part which has more than one element.
a(n) is the number of chains of length 2 from the top element to the bottom element in the partition lattice on n labeled objects.
(End)

			For n = 3 there are a(3) = 3 proper partitions of {1,2,3}, which can be represented {12|3}, {13|2}, {23|1}.
For n = 4 there are a(4) = 13 proper partitions of {1,2,3,4}, which can be represented {123|4}, {124|3}, {134|2}, {234|1}, {12|34}, {13|24}, {14|23}, {12|3|4}, {13|2|4}, {14|2|3}, {23|1|4}, {24|1|3}, {34|1|2}.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 148.

Vincenzo Librandi, Table of n, a(n) for n = 2..200
Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7. See Table I (it is not certain that this is the same sequence. - _N. J. A. Sloane_, Jun 25 2015)
Ivo Rosenberg and N. J. A. Sloane, Correspondence, 1971

Cf. A000110, A008826.

List([3..30], n-> Bell(n)-2); # G. C. Greubel, Sep 13 2019

[Bell(n) -2: n in [3..30]]; // G. C. Greubel, Sep 13 2019

seq(combinat[bell](n)-2, n=2..31); # Zerinvary Lajos, Sep 29 2006

Table[BellB[n] - 2, {n, 3, 30}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

a(n)=sum(j=2,n--,(j+1)*stirling(n,j,2)) \\ Charles R Greathouse IV, Jul 06 2011

[bell_number(n)-2 for n in (3..30)] # G. C. Greubel, Sep 13 2019

a(n) = A000110(n) - 2.

More terms from Vladeta Jovovic, Jan 02 2004

Name changed and a(2)=0 prepended by Harry Richman, Mar 18 2023

A002826 Number of precomplete Post functions of n variables.

Original entry on oeis.org

1, 5, 18, 82, 643, 15182, 7848984, 549761932909, 10626621620680478174719, 1701411834605079120446041612364090304458, 79607061350691085453966118726400345961810854094316840855510985236799831016092

Offset: 1

N. J. A. Sloane

nonn

S. V. Jablonskii, Some results in the theory of functional systems (Russian), in Proceedings of the International Congress of Mathematicians (Helsinki, 1978), pp. 963-971, Acad. Sci. Fennica, Helsinki, 1980.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 1969 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

Cf. A002824, A002825, A008827, A246069, A246137, A246417.

a(n) = A002824(n) + A246069(n) + A246137(n) + A008827(n) + A002825(n) + A246417(n). - Sean A. Irvine, Aug 25 2014

More terms from Sean A. Irvine, Aug 25 2014

A002825 Number of precomplete Post functions.

Original entry on oeis.org

1, 2, 9, 40, 355, 11490, 7758205, 549758283980, 10626621620680257450759, 1701411834605079120446041612344662275078, 79607061350691085453966118726400345961810854094316840855510985234351715774913

Offset: 1

N. J. A. Sloane

nonn

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 1969 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

Alois P. Heinz, Table of n, a(n) for n = 1..14
Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
Ivo Rosenberg and N. J. A. Sloane, Correspondence, 1971
Zhi-Hong Sun, Congruences for Apéry-like numbers, arXiv:1803.10051 [math.NT], 2018.
E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

a[1] = 1; a[n_] := -n-2+(-1)^(n-1) Sum[(-1)^k Binomial[n, k] Sum[2^Binomial[ k, j], {j, 0, k}], {k, 0, n-1}];
Array[a, 11] (* Jean-François Alcover, Aug 19 2018 *)

a(n) = if (n==1, 1, -n - 2 + (-1)^(n-1) * sum(k=0, n-1, (-1)^k * binomial(n, k) * sum(j=0, k, (2^binomial(k, j))))); \\ Michel Marcus, Aug 25 2014

a(1) = 1. a(n) = -n - 2 + (-1)^(n-1) * Sum_{k=0..n-1} ((-1)^k * binomial(n, k) * Sum_{j=0..k} 2^binomial(k, j)), n > 1. - Sean A. Irvine, Aug 24 2014

More terms from Sean A. Irvine, Aug 24 2014

A246069 Number of maximal classes determined by permutations.

Original entry on oeis.org

0, 1, 1, 3, 6, 35, 120, 105, 1120, 19089, 362880, 133595, 39916800, 148397535, 458313856, 2027025, 1307674368000, 6133352225, 355687428096000, 40549021532019, 4139906028544000, 464463124401214575, 51090942171709440000, 1173011341727225

Offset: 1

Sean A. Irvine, Aug 25 2014

nonn

Corresponds to r_2(k) in the Rosenberg paper.

Alois P. Heinz, Table of n, a(n) for n = 1..450
Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
Ivo Rosenberg and N. J. A. Sloane, Correspondence, 1971

Cf. A002826.

a:= n -> add(n!/((n/p)! * p^(n/p) * (p-1)), p = numtheory:-factorset(n)):
seq(a(n), n=1..100); # Robert Israel, Aug 27 2014

a[n_] := If[n == 1, 0, Sum[n!/((n/p)! p^(n/p) (p-1)), {p, FactorInteger[n][[All, 1]]}]]; Array[a, 100] (* Jean-François Alcover, Mar 22 2019, after Robert Israel *)

a(n) = sum(n! / (m! * p^m * (p-1)), n = p * m, p prime). (corrected by Robert Israel, Aug 27 2014)

A246417 Homomorphic inverse images of elementary h-ary relations.

Original entry on oeis.org

0, 0, 1, 7, 36, 171, 813, 4012, 25931, 342263, 6498746, 116477549, 1839530421, 26071946330, 339710531761, 4165394873379, 50578180795388, 717354862704287, 15348610400624113, 466529833772501084, 15332096138370552335

Offset: 1

Sean A. Irvine, Aug 25 2014

nonn

Corresponds to r_6(k) in the Rosenberg paper.

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
Ivo Rosenberg and N. J. A. Sloane, Correspondence, 1971
E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

Cf. A002826.

a(n) = Sum_{h^m <= k, h >= 3, m >= 1} (((-1)^h / (m! * (h!)^m)) * Sum_{L=1..h^m} (-1)^L * binomial(h^m, L) * L^n). - Sean A. Irvine, Aug 25 2014

A259337 Classes of self-dual precomplete Post functions.

Original entry on oeis.org

1, 1, 1, 24, 11, 720

Offset: 2

N. J. A. Sloane, Jun 25 2015

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

A259338 Classes of type U precomplete Post functions.

Original entry on oeis.org

0, 3, 13, 50, 190, 917

Offset: 2

N. J. A. Sloane, Jun 25 2015

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

A259339 Erroneous version of A002825.

Original entry on oeis.org

1, 2, 9, 40, 355, 11490, 7758233, 549758283756

Offset: 1

N. J. A. Sloane, Jun 02 2017

dead

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

cp's OEIS Frontend

A259336 Erroneous version of A002824.

Views

Author

Keywords

References

Links

A001035 Number of partially ordered sets ("posets") with n labeled elements (or labeled acyclic transitive digraphs).

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A008827 Number of proper partitions of a set of n labeled elements.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

Extensions

A002826 Number of precomplete Post functions of n variables.

Views

Author

Keywords

References

Links

Crossrefs

Formula

Extensions

A002825 Number of precomplete Post functions.

Views

Author

Keywords

References

Links

Programs

Mathematica

PARI

Formula

Extensions

A246069 Number of maximal classes determined by permutations.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A246417 Homomorphic inverse images of elementary h-ary relations.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Formula

A259337 Classes of self-dual precomplete Post functions.

Views