cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A056090 Number of 4-element ordered antichain covers of an unlabeled n-element set.

Original entry on oeis.org

25, 429, 3364, 17602, 71385, 242347, 720792, 1934076, 4777337, 11021713, 24008532, 49790614, 98954626, 189457350, 350941064, 631167840, 1105440045, 1890167329, 3162113836, 5185330818, 8348369731, 13215102985, 20593381200, 31626858540, 47916657405, 71681161365
Offset: 4

Views

Author

Vladeta Jovovic, Goran Kilibarda, Jul 27 2000

Keywords

References

  • V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
  • V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Links

Crossrefs

Cf. A056047 for 4-antichain (unordered) covers of a labeled n-set, A051112. See also A056074, A056093.

Programs

  • Magma
    [(-104270181120*n + 236073062016*n^2 - 169534943760*n^3 + 28403538800*n^4 + 12862329480*n^5 - 2983956976*n^6 - 613678065*n^7 + 39763295*n^8 + 21456435*n^9 + 2461459*n^10 + 143325*n^11 + 5005*n^12 + 105*n^13 + n^14)/Factorial(14): n in [4..50]]; // G. C. Greubel, Oct 06 2017
  • Mathematica
    Table[(-104270181120 n + 236073062016 n^2 - 169534943760 n^3 + 28403538800 n^4 + 12862329480 n^5 - 2983956976 n^6 - 613678065 n^7 + 39763295 n^8 + 21456435 n^9 + 2461459 n^10 + 143325 n^11 + 5005 n^12 + 105 n^13 + n^14)/(14)!, {n, 4, 50}] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1},{25,429,3364,17602,71385,242347,720792,1934076,4777337,11021713,24008532,49790614,98954626,189457350,350941064},30] (* Harvey P. Dale, Dec 09 2021 *)
  • PARI
    for(n=4,50, print1((-104270181120*n + 236073062016*n^2 - 169534943760*n^3 + 28403538800*n^4 + 12862329480*n^5 - 2983956976*n^6 - 613678065*n^7 + 39763295*n^8 + 21456435*n^9 + 2461459*n^10 + 143325*n^11 + 5005*n^12 + 105*n^13 + n^14)/(14)!, ", ")) \\ G. C. Greubel, Oct 06 2017

Formula

a(n) = C(n + 14, 14) - 12*C(n + 10, 10) + 24*C(n + 8, 8) + 4*C(n + 7, 7) - 18*C(n + 6, 6) + 6*C(n + 5, 5) - 36*C(n + 4, 4) + 36*C(n + 3, 3) + 11*C(n + 2, 2) - 22*C(n + 1, 1) + 6*C(n, 0).
G.f.: x^4*(6*x^10 -62*x^9 +271*x^8 -636*x^7 +800*x^6 -328*x^5 -495*x^4 +812*x^3 -446*x^2 +54*x +25)/(1-x)^15. - Colin Barker, May 29 2012
a(n) = (-104270181120 n + 236073062016 n^2 - 169534943760 n^3 + 28403538800 n^4 + 12862329480 n^5 - 2983956976 n^6 - 613678065 n^7 + 39763295 n^8 + 21456435 n^9 + 2461459 n^10 + 143325 n^11 + 5005 n^12 + 105 n^13 + n^14)/(14)!. - G. C. Greubel, Oct 06 2017

A056093 Number of 5-element ordered antichain covers of an unlabeled n-element set.

Original entry on oeis.org

30, 2176, 54036, 709956, 6290051, 42606671, 237197942, 1135834242, 4823607212, 18563958502, 65783057592, 217240417628, 674884181813, 1987124979703, 5579019610088, 15010371955248, 38862554420034, 97163223921924, 235290234202584, 553296290481584
Offset: 4

Views

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 27 2000

Keywords

References

  • V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Links

Crossrefs

Cf. A056048 for 5-antichain (unordered) covers of a labeled n-set, A051113. See also A056074, A056090.

Programs

  • Mathematica
    Table[Binomial[n+30,30]-20 Binomial[n+22,22]+60 Binomial[n+18,18]+ 20 Binomial[n+16,16]+ 10 Binomial[n+15,15]-110 Binomial[n+14,14]- 120 Binomial[n+13,13]+ 150 Binomial[n+12,12]+ 120 Binomial[n+11,11]- 240 Binomial[n+10,10]+ 20 Binomial[n+9,9]+ 240 Binomial[n+8,8]+ 40 Binomial[n+7,7]- 205 Binomial[n+6,6]+ 60 Binomial[n+5,5]- 210 Binomial[n+4,4]+ 210 Binomial[n+3,3]+ 50 Binomial[n+2,2]- 100 Binomial[n+1,1]+ 24 Binomial[n,0],{n,4,30}] (* Harvey P. Dale, Sep 06 2011 *)

Formula

a(n)=C(n + 30, 30) - 20*C(n + 22, 22) + 60*C(n + 18, 18) + 20*C(n + 16, 16) + 10*C(n + 15, 15) - 110*C(n + 14, 14) - 120*C(n + 13, 13) + 150*C(n + 12, 12) + 120*C(n + 11, 11) - 240*C(n + 10, 10) + 20*C(n + 9, 9) + 240*C(n + 8, 8) + 40*C(n + 7, 7) - 205*C(n + 6, 6) + 60*C(n + 5, 5) - 210*C(n + 4, 4) + 210*C(n + 3, 3) + 50*C(n + 2, 2) - 100*C(n + 1, 1) + 24*C(n, 0).

Extensions

More terms from Harvey P. Dale, Sep 06 2011

A056164 Number of ordered antichain covers of an unlabeled n-set; labeled T_1-hypergraphs (without empty hyperedges) with n hyperedges.

Original entry on oeis.org

1, 2, 6, 109, 191177
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Jul 31 2000

Keywords

Comments

A T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair of distinct nodes has a hyperedge containing one but not the other node.

Examples

			There are 6 ordered antichain covers on an unlabeled 3-set: ({1,2,3}), ({1},{2,3}), ({2,3},{1}), ({1,2},{1,3}), ({1},{2},{3}), ({1,2},{1,3},{2,3}).
a(3)=1+3+2=6; a(4)=1+6+17+25+30+30=109; a(5)=1+10+71+429+2176+8310+20580+38640+60480+60480=191177.

References

  • V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
  • V. Jovovic and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Links

Crossrefs

Cf. A056074, A056090, A056093, A000372, A056005, A056069-A056071, A056073, A056046-A056049, A056052, A056101, A056104, A051112-A051118.

Formula

a(n)=Sum_{k=1..C(n, floor(n/2))}b(k, n) where b(k, n) is the number of k-element ordered antichains covers of an unlabeled n-set.
Showing 1-3 of 3 results.

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