A051185 -id:A051185 - cp's OEIS frontend

A305843 Number of labeled spanning intersecting set-systems on n vertices.

1, 1, 3, 27, 1245, 1308285, 912811093455, 291201248260060977862887, 14704022144627161780742038728709819246535634969, 12553242487940503914363982718112298267975272588471811456164576678961759219689708372356843289

Offset: 0

Gus Wiseman, Jun 11 2018

nonn

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge.

			The a(3) = 27 spanning intersecting set-systems:
{{1,2,3}}
{{1},{1,2,3}}
{{2},{1,2,3}}
{{3},{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,2},{1,2,3}}
{{1,3},{2,3}}
{{1,3},{1,2,3}}
{{2,3},{1,2,3}}
{{1},{1,2},{1,3}}
{{1},{1,2},{1,2,3}}
{{1},{1,3},{1,2,3}}
{{2},{1,2},{2,3}}
{{2},{1,2},{1,2,3}}
{{2},{2,3},{1,2,3}}
{{3},{1,3},{2,3}}
{{3},{1,3},{1,2,3}}
{{3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,2,3}}
{{1,2},{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1},{1,2},{1,3},{1,2,3}}
{{2},{1,2},{2,3},{1,2,3}}
{{3},{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}

Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305844.

Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#==Range[n],FreeQ[Intersection@@@Tuples[#,2],{}]]&],{n,1,4}]

Inverse binomial transform of A051185.

A305854 Number of unlabeled spanning intersecting set-systems on n vertices.

Original entry on oeis.org

1, 1, 2, 10, 110, 14868, 1289830592

Offset: 0

Gus Wiseman, Jun 11 2018

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge.

			Non-isomorphic representatives of the a(3) = 10 spanning intersecting set-systems:
  {{1,2,3}}
  {{3},{1,2,3}}
  {{1,3},{2,3}}
  {{2,3},{1,2,3}}
  {{3},{1,3},{2,3}}
  {{3},{2,3},{1,2,3}}
  {{1,2},{1,3},{2,3}}
  {{1,3},{2,3},{1,2,3}}
  {{3},{1,3},{2,3},{1,2,3}}
  {{1,2},{1,3},{2,3},{1,2,3}}

Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305855-A305857.

a(n) = A305856(n) - A305856(n-1) for n > 0. - Andrew Howroyd, Aug 12 2019

a(5) from Andrew Howroyd, Aug 12 2019

a(6) from Bert Dobbelaere, Apr 28 2025

A305844 Number of labeled spanning intersecting antichains on n vertices.

Original entry on oeis.org

1, 1, 1, 5, 50, 2330, 1407712, 229800077244, 423295097236295093695

Offset: 0

Gus Wiseman, Jun 11 2018

nonn

An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other. S is spanning if every vertex is contained in some edge.

			The a(3) = 5 spanning intersecting antichains:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}

Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Cf. A001206, A006126, A048143, A051185, A134958, A030019, A304985, A305843.

Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#==Range[n],FreeQ[Intersection@@@Tuples[#,2],{},{1}],Select[Tuples[#,2],UnsameQ@@#&&Complement@@#=={}&]=={}]&],{n,1,4}]

Inverse binomial transform of A001206(n + 1).

A036239 Number of 2-element intersecting families of an n-element set; number of 2-way interactions when 2 subsets of power set on {1..n} are chosen at random.

Original entry on oeis.org

0, 2, 15, 80, 375, 1652, 7035, 29360, 120975, 494252, 2007555, 8120840, 32753175, 131818052, 529680075, 2125927520, 8525298975, 34165897052, 136857560595, 548011897400, 2193792030375, 8780400395252, 35137296305115, 140596265198480

Offset: 1

N. J. A. Sloane

Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 1) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x. - Ross La Haye, Jan 10 2008

Graph theory formulation. Let P(A) be the power set of an n-element set A. Then a(n) = the number of edges in the intersection graph G of P(A). The vertices of G are the elements of P(A) and the edges of G are the pairs of elements {x,y} of P(A) such that x and y are intersecting (and x <> y). - Ross La Haye, Dec 23 2017

W. W. Kokko, "Interactions", manuscript, 1983.

T. D. Noe, Table of n, a(n) for n = 1..200
Taylor Brysiewicz, Holger Eble, and Lukas Kühne, Enumerating chambers of hyperplane arrangements with symmetry, arXiv:2105.14542 [math.CO], 2021.
V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, in Russian, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, English translation, in Discrete Mathematics and Applications, 9, (1999), no. 6.
Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).
Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Cf. A036240, A051180-A051185, A028243, A032263.

Cf. A003462, A006516, A016127, A016129, A016130, A016311, A016316, A016321, A016325. - Zerinvary Lajos, Jun 05 2009

LinearRecurrence[{10,-35,50,-24},{0,2,15,80},40] (* or *) With[{c=1/2!}, Table[ c(4^n-3^n-2^n+1),{n,40}]] (* Harvey P. Dale, May 11 2011 *)

a(n)=(4^n-3^n-2^n+1)/2 \\ Charles R Greathouse IV, Jul 25 2011

[(4^n - 2^n)/2-(3^n - 1)/2 for n in range(1,24)] # Zerinvary Lajos, Jun 05 2009

a(n) = (1/2) * (4^n - 3^n - 2^n + 1).
a(n) = 3*Stirling2(n+1,4) + 2*Stirling2(n+1,3). - Ross La Haye, Jan 10 2008
a(n) = A006516(n) - A003462(n). - Zerinvary Lajos, Jun 05 2009
From Harvey P. Dale, May 11 2011: (Start)
a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(0)=0, a(1)=2, a(2)=15, a(3)=80.
G.f.: x^2*(2-5*x)/(1 - 10*x + 35*x^2 - 50*x^3 + 24*x^4). (End)
E.g.f.: exp(x)*(exp(x) - 1)^2*(exp(x) + 1)/2. - Stefano Spezia, Jun 26 2022

A318717 Number of strict integer partitions of n in which no two parts are relatively prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 5, 1, 5, 4, 6, 1, 10, 1, 11, 6, 12, 1, 19, 3, 18, 8, 23, 1, 36, 2, 32, 13, 38, 7, 57, 2, 54, 19, 68, 3, 95, 3, 90, 33, 104, 3, 148, 7, 149, 40, 166, 5, 230, 17, 226, 56, 256, 6, 360, 9, 340, 84, 390, 25, 527, 11, 513, 109

Offset: 0

Gus Wiseman, Sep 02 2018

nonn

			The a(20) = 11 partitions:
  (20),
  (12,8), (14,6), (15,5), (16,4), (18,2),
  (10,6,4), (10,8,2), (12,6,2), (14,4,2),
  (8,6,4,2).

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600

Cf. A000009, A007359, A007360, A051185, A302569, A302797, A303140, A303280, A303283, A305713, A305843, A305854, A305713, A318715, A318719.

Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,And@@(GCD[##]>1&)@@@Select[Tuples[#,2],Less@@#&]]&]],{n,30}]

a(51)-a(69) from Alois P. Heinz, Sep 02 2018

A001206 Number of self-dual monotone Boolean functions of n variables.

Original entry on oeis.org

0, 1, 2, 4, 12, 81, 2646, 1422564, 229809982112, 423295099074735261880

Offset: 0

N. J. A. Sloane

Sometimes called Hosten-Morris numbers (or HM numbers).
Also the number of simplicial complexes on the set {1, ..., n-1} such that no pair of faces covers all of {1, ..., n-1}. [Miller-Sturmfels] - N. J. A. Sloane, Feb 18 2008
Also the maximal number of generators of a neighborly monomial ideal in n variables. [Miller-Sturmfels]. - N. J. A. Sloane, Feb 18 2008
Also the number of intersecting antichains on a labeled (n-1)-set or (n-1)-variable Boolean functions in the Post class F(7,2). Cf. A059090. - Vladeta Jovovic, Goran Kilibarda, Dec 28 2000
Also the number of nondominated coteries on n members. - Don Knuth, Sep 01 2005
The number of maximal families of intersecting subsets of an n-element set. - Bridget Tenner, Nov 16 2006
Rivière gives a(n) for n <= 5. - N. J. A. Sloane, May 12 2012

			a(2) = 1 + 1 = 2;
a(3) = 1 + 3 = 4;
a(4) = 1 + 7 + 3 + 1 = 12;
a(5) = 1 + 15 + 30 + 30 + 5 = 81;
a(6) = 1 + 31 + 195 + 605 + 780 + 543 + 300 + 135 + 45 + 10 + 1 = 2646;
a(7) = 1 + 63 + 1050 + 9030 + 41545 + 118629 + 233821 + 329205 + 327915 + 224280 + 100716 + 29337 + 5950 + 910 + 105 + 1 = 1422564.
Cf. A059090.
From _Gus Wiseman_, Jul 03 2019: (Start)
The a(1) = 1 through a(4) = 12 intersecting antichains of nonempty sets (see Jovovic and Kilibarda's comment):
  {}  {}     {}       {}
      {{1}}  {{1}}    {{1}}
             {{2}}    {{2}}
             {{1,2}}  {{3}}
                      {{1,2}}
                      {{1,3}}
                      {{2,3}}
                      {{1,2,3}}
                      {{1,2},{1,3}}
                      {{1,2},{2,3}}
                      {{1,3},{2,3}}
                      {{1,2},{1,3},{2,3}}
(End)

Martin Aigner and Günter M. Ziegler, Proofs from THE BOOK, Third Edition, Springer-Verlag, 2004. See chapter 22.
V. Jovovic and G. Kilibarda, The number of n-variable Boolean functions in the Post class F(7,2), Belgrade, 2001, in preparation.
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
W. F. Lunnon, The IU function: the size of a free distributive lattice, pp. 173-181 of D. J. A. Welsh, editor, Combinatorial Mathematics and Its Applications. Academic Press, NY, 1971.
Charles F. Mills and W. M. Mills, The calculation of λ(8), preprint, 1979. Gives a(8).
E. Miller and B. Sturmfels, Combinatorial Commutative Algebra, Springer, 2005.
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).

Taras Banakh, Volodymyr Gavrylkiv, Automorphism groups of superextensions of groups, arXiv:1802.05804 [math.GR], 2018.
Jan C. Bioch and Toshihide Ibaraki, Generating and approximating nondominated coteries, IEEE Transactions on parallel and distributed systems 6 (1995), 905-914.
A. E. Brouwer and A. Verbeek, Counting families of mutually intersecting sets, Report ZN 41, March 1972, Math. Centr., Amsterdam. Gives a(n) for n <= 7.
A. E. Brouwer and A. Verbeek, Counting families of mutually intersecting sets, Electronic Journal of Combinatorics, Volume 20, Issue 2 (2013), Paper #P8.
Gábor Damásdi, Stefan Felsner, António Girão, Balázs Keszegh, David Lewis, Dániel T. Nagy, Torsten Ueckerdt, On Covering Numbers, Young Diagrams, and the Local Dimension of Posets, arXiv:2001.06367 [math.CO], 2020.
Jesús A. De Loera, Serkan Hoşten, Robert Krone, Lily Silverstein, Average Behavior of Minimal Free Resolutions of Monomial Ideals, arXiv:1802.06537 [math.AC], 2018.
Serkan Hosten and Walter D. Morris, Jr., The order dimension of the complete graph, Discrete Math. 201 (1999), pp. 133-139.
D. E. Loeb, Challenges in playing multiplayer games, in Levy and Beal, editors, Heuristic Programming in Artificial Intelligence, vol. 4, Ellis Horwood, 1994. [broken link]
D. E. Loeb and A. Meyerowitz, The maximal intersecting family of sets graph, in H. Barcelo and G. Kalai, editors, Proceedings of the Conference on Jerusalem Combinatorics 1993. AMS series Contemporary Mathematics, 1994.
Bartłomiej Pawelski, Counting and generating monotone Boolean functions, Doctoral Diss., Univ. Gdańsk, (Poland, 2024). See pp. 12, 15, 38, 49, 58, 73.
Bartlomiej Pawelski and Andrzej Szepietowski, Divisibility properties of Dedekind numbers, arXiv:2302.04615 [math.CO], 2023.
N. M. Rivière, Recursive formulas on free distributive lattices, J. Combinatorial Theory 5 1968 229--234. MR0231764 (38 #92).
Tom Trotter, An Application of the Erdős/Stone Theorem, Slides, Sept. 13, 2001.
Index entries for sequences related to Boolean functions

Cf. A000372, A059090.
The case with empty edges allowed is A326372.
The maximal case is A007363, or A326363 with empty edges allowed.
The case with empty intersection is A326366.
The inverse binomial transform is the covering case A305844.
Cf. A006126, A014466, A051185, A326361, A326362.

stableSets[u_,Q_]:=If[Length[u]==0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r==w||Q[r,w]||Q[w,r]],Q]]]];
Table[Length[stableSets[Subsets[Range[n],{1,n}],Or[Intersection[#1,#2]=={},SubsetQ[#1,#2]]&]],{n,0,5}] (* Gus Wiseman, Jul 03 2019 *)

a(n+1) = Sum_{m=0..A037952(n)} A059090(n, m).

For n > 0, a(n) = A326372(n - 1) - 1. - Gus Wiseman, Jul 03 2019

a(8) due to C. F. Mills & W. H. Mills, 1979
a(8) from Daniel E. Loeb, Jan 04 1996
a(8) confirmed by Don Knuth, Feb 08 2008
a(9) from Andries E. Brouwer, Aug 25 2012

A051180 Number of 3-element intersecting families of an n-element set.

Original entry on oeis.org

0, 0, 0, 13, 222, 2585, 25830, 238833, 2111382, 18142585, 152937510, 1271964353, 10476007542, 85662034185, 696700867590, 5643519669073, 45575393343702, 367206720319385, 2953481502692070, 23723872215168993, 190372457332919862

Offset: 0

Vladeta Jovovic, Goran Kilibarda

G. C. Greubel, Table of n, a(n) for n = 0..1000
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, in Russian, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, English translation, in Discrete Mathematics and Applications, 9, (1999), no. 6.
Index entries for linear recurrences with constant coefficients, signature (29,-343,2135,-7504,14756,-14832,5760).

Cf. A036239, A051181-A051185.

seq(1/3!*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2),n=0..40);

Table[1/3!(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2),{n,0,30}] (* or *) LinearRecurrence[{29,-343,2135,-7504,14756,-14832,5760},{0,0,0,13,222,2585,25830},30] (* Harvey P. Dale, Jul 07 2013 *)

for(n=0,25, print1((1/3!)*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2), ", ")) \\ G. C. Greubel, Oct 06 2017

a(n) = (1/3!)*(8^n - 3*6^n + 3*5^n - 4*4^n + 3*3^n + 2*2^n - 2).
G.f. x^3*(744*x^3 - 606*x^2 + 155*x - 13)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Jul 29 2012
a(0)=0, a(1)=0, a(2)=0, a(3)=13, a(4)=222, a(5)=2585, a(6)=25830, a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7). - Harvey P. Dale, Jul 07 2013

More terms from Sascha Kurz, Mar 25 2002

A318715 Number of strict integer partitions of n with relatively prime parts in which no two parts are relatively prime.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 1, 0, 4, 0, 3, 0, 1, 0, 5, 0, 8, 0, 2, 0, 5, 0, 10, 0, 4, 0, 13, 0, 15, 0, 3, 1, 13, 0, 19, 0, 9, 1, 24, 0, 20

Offset: 1

Gus Wiseman, Sep 02 2018

nonn

			The a(67) = 10 strict integer partitions are
  (45,12,10) (42,15,10) (40,15,12) (33,22,12) (28,21,18)
  (36,15,10,6) (30,15,12,10) (28,21,12,6) (24,18,15,10)
  (24,15,12,10,6).

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..500

Cf. A007359, A051185, A078374, A303140, A303282, A303283, A305713, A305843, A305854, A318716, A318717, A318720.

Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,GCD@@#==1,And@@(GCD[##]>1&)@@@Select[Tuples[#,2],Less@@#&]]&]],{n,50}]

a(71)-a(85) from Robert Price, Sep 08 2018

A305857 Number of unlabeled intersecting antichains on up to n vertices.

Original entry on oeis.org

1, 2, 3, 6, 15, 87, 3528, 47174113

Offset: 0

Gus Wiseman, Jun 11 2018

An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other.

			Non-isomorphic representatives of the a(4) = 15 intersecting antichains:
  {}
  {{1}}
  {{1,2}}
  {{1,2,3}}
  {{1,2,3,4}}
  {{1,3},{2,3}}
  {{1,4},{2,3,4}}
  {{1,3,4},{2,3,4}}
  {{1,2},{1,3},{2,3}}
  {{1,4},{2,4},{3,4}}
  {{1,3},{1,4},{2,3,4}}
  {{1,2},{1,3,4},{2,3,4}}
  {{1,2,4},{1,3,4},{2,3,4}}
  {{1,2},{1,3},{1,4},{2,3,4}}
  {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

Cf. A001206, A006126, A051185, A261006, A283877, A304998, A305843, A305844, A305854, A305855, A305856.

a(n) = A305855(0) + A305855(1) + ... + A305855(n). - Brendan McKay, May 11 2020

a(6) from Andrew Howroyd, Aug 13 2019

a(7) from Brendan McKay, May 11 2020

A337667 Number of compositions of n where any two parts have a common divisor > 1.

Original entry on oeis.org

1, 0, 1, 1, 2, 1, 5, 1, 8, 4, 17, 1, 38, 1, 65, 19, 128, 1, 284, 1, 518, 67, 1025, 1, 2168, 16, 4097, 256, 8198, 1, 16907, 7, 32768, 1027, 65537, 79, 133088, 19, 262145, 4099, 524408, 25, 1056731, 51, 2097158, 16636, 4194317, 79, 8421248, 196, 16777712

Offset: 0

Gus Wiseman, Oct 05 2020

nonn

First differs from A178472 at a(31) = 7, a(31) = 1.

			The a(2) = 1 through a(10) = 17 compositions (A = 10):
   2   3   4    5   6     7   8      9     A
           22       24        26     36    28
                    33        44     63    46
                    42        62     333   55
                    222       224          64
                              242          82
                              422          226
                              2222         244
                                           262
                                           424
                                           442
                                           622
                                           2224
                                           2242
                                           2422
                                           4222
                                           22222

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..290

A101268 = 1 + A337462 is the pairwise coprime version.
A328673 = A200976 + 1 is the unordered version.
A337604 counts these compositions of length 3.
A337666 ranks these compositions.
A337694 gives Heinz numbers of the unordered version.
A337983 is the strict case.
A051185 counts intersecting set-systems, with spanning case A305843.
A318717 is the unordered strict case.
A319786 is the version for factorizations, with strict case A318749.
A327516 counts pairwise coprime partitions.
A333227 ranks pairwise coprime compositions.
A333228 ranks compositions whose distinct parts are pairwise coprime.
Cf. A051424, A082024, A178472, A284825, A319752, A327039, A337599, A337605, A337665.

stabQ[u_,Q_]:=And@@Not/@Q@@@Tuples[u,2];
Table[Length[Join@@Permutations/@Select[IntegerPartitions[n],stabQ[#,CoprimeQ]&]],{n,0,15}]

cp's OEIS Frontend

A305843 Number of labeled spanning intersecting set-systems on n vertices.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

A305854 Number of unlabeled spanning intersecting set-systems on n vertices.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

Extensions

A305844 Number of labeled spanning intersecting antichains on n vertices.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A036239 Number of 2-element intersecting families of an n-element set; number of 2-way interactions when 2 subsets of power set on {1..n} are chosen at random.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

A318717 Number of strict integer partitions of n in which no two parts are relatively prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A001206 Number of self-dual monotone Boolean functions of n variables.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A051180 Number of 3-element intersecting families of an n-element set.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions

A318715 Number of strict integer partitions of n with relatively prime parts in which no two parts are relatively prime.