A011828 -id:A011828 - cp's OEIS frontend

A007695 Cardinalities of Sperner families on 1,...,n.

2, 3, 5, 10, 26, 96, 553, 5461, 100709, 3718354, 289725509, 49513793526, 19089032278261, 16951604697397302, 35231087224279091310, 173550485517380958360611, 2047581288200721764035942914

Offset: 0

N. J. A. Sloane, Don Knuth

Also number of f-vectors for simplicial complexes on at most n vertices.

S. Johnson, Upper bounds for constant weight error correcting codes, Discrete Math., 3 (1972), 109-124.
D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3 (p. 743).
D. E. Knuth, Art of Computer Programming, Vol. 4, Section 7.3, to appear.
S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. Knuth, Email to N. J. A. Sloane, Aug. 1994.
Tamon Stephen and Timothy Yusun, Counting inequivalent monotone Boolean functions, arXiv preprint arXiv:1209.4623 [cs.DS], 2012.

This is the limiting form of A011828-A011833.

Cf. A001405.

c[ 0, 0 ]=1; c[ 0, 1 ]=1; kap[ 0, 0 ]=0; f[ n_ ] := Block[ {s=2, r, d, k, j}, For[ r=1, r<=n, r++, d=s; k=r; j=0; s=0;
For[ x=0, x<=Binomial[ n, r ], x++, If[ x>=Binomial[ k, r ], k++, 0 ]; kap[ r, x ]=If[ x==0, 0, Binomial[ k-1, r-1 ]+kap[ r-1, x-Binomial[ k-1, r ] ] ];
While[ j

Entry revised by N. J. A. Sloane, Sep 03 2011

A011820 Number of M-sequences m_0,...,m_4 with m_1 < n.

Original entry on oeis.org

2, 6, 32, 203, 1144, 5345, 20926, 70506, 209746, 562727, 1384758, 3167606, 6807620, 13863904, 26941700, 50245591, 90358146, 157312324, 266040452, 438299013, 705186944, 1110395771, 1714352818, 2599444040, 3876530866

Offset: 0

Svante Linusson (linusson(AT)math.kth.se)

S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A011819-A011825, A011828.

a(n)=n*(4*n^9+61*n^8+408*n^7+1722*n^6+6132*n^5+18333*n^4+41072*n^3 +88748*n^2 +133824*n+193536)/120960+2 \\ Charles R Greathouse IV, Dec 08 2011

a(n) = ( 4*n^10 +61*n^9 +408*n^8 +1722*n^7 +6132*n^6 +18333*n^5 +41072*n^4 +88748*n^3 +133824*n^2 +193536*n +241920 )/120960. - Frank Ellermann

G.f.: -x*(x^10 -11*x^9 +53*x^8 -147*x^7 +268*x^6 -298*x^5 +341*x^4 -149*x^3 +76*x^2 -16*x +2) / (x-1)^11. - Colin Barker, Feb 15 2014

A011829 Number of f-vectors for simplicial complexes of dimension at most 4 on at most n-1 vertices.

Original entry on oeis.org

2, 3, 5, 10, 26, 96, 552, 4908, 48230, 398663, 2631241, 14192097, 64663638, 256174350, 902972232, 2883651027, 8463753978, 23094833355, 59133598085, 143164108028, 329810868994, 726833391860, 1539215246944, 3144340388550

Offset: 1

Svante Linusson (linusson(AT)math.kth.se)

nonn

Apparently a polynomial (n^15)/32659200 + .... [Frank Ellermann]

D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3 (p. 743).
S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.

Cf. A011828, A011830, A011831, A011832, A011833, A007695.

Empirical G.f.: -x*(x^15 -16*x^14 +114*x^13 -1154*x^12 -2541*x^11 -16919*x^10 -6585*x^9 -17282*x^8 +9460*x^7 -8548*x^6 +5196*x^5 -2426*x^4 +830*x^3 -197*x^2 +29*x -2)/(x -1)^16. [Colin Barker, Sep 18 2012]

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A007695 Cardinalities of Sperner families on 1,...,n.

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A011820 Number of M-sequences m_0,...,m_4 with m_1 < n.

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A011829 Number of f-vectors for simplicial complexes of dimension at most 4 on at most n-1 vertices.

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