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 1-5 of 5 results.

A110058 Number of nonnegative integer matrices of order n for which all row and column sums equal n.

Original entry on oeis.org

1, 1, 3, 55, 10147, 22069251, 602351808741, 215717608046511873, 1046591482728407939338275, 70417932475495769964322670258947, 66880713903767740581650957184096513655153, 909176713758393122455793478657031533216492953328933, 178876969166665269546249744608783223036842010760723370462856181, 514016665650183402309555825250370336139392333285719205357202846243695510965
Offset: 0

Views

Author

Brendan McKay, Sep 04 2005

Keywords

Comments

Computed by a method that involves summing a multivariate generating function over roots of unity.

Examples

			a(2) = 3 due to the matrices [1,1 | 1,1], [0,2 | 2,0] and [2,0 | 0,2].

Links

Crossrefs

Cf. A058407, A058410, A058391.
Main diagonal of A257493 and A333901.

Programs

  • Sage
    from sage.combinat.integer_matrices import IntegerMatrices
[IntegerMatrices([n]*n, [n]*n).cardinality() for n in (0..6)] # Freddy Barrera, Dec 27 2018

Formula

log a(n) = 2(log 2)*n^2 - n*(log n) - n*(log 4*Pi) + (log n) + O(1). - Igor Pak, May 15 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Apr 26 2015

A058408 Number of 3 X n nonnegative integer matrices with all column sums 4, up to row and column permutation.

Original entry on oeis.org

1, 4, 26, 129, 546, 2010, 6615, 19650, 53790, 137035, 328262, 745078, 1613072, 3348198, 6693822, 12937656, 24253200, 44219610, 78604130, 136511100, 232054284
Offset: 0

Views

Author

Vladeta Jovovic, Nov 25 2000

Keywords

Comments

Number of 3 X n nonnegative integer matrices with all column sums equal to m, up to row and column permutation, is coefficient of x^n in expansion of 1 / 6 * (1 / (1 - x)^C(m + 2,2) + 3 / (1 - x)^floor((m + 2) / 2) / (1 - x^2)^(C(m + 2,2) - floor((m + 2) / 2)) / 2 + 2 / (1 - x)^(C(m + 2,2) - 3 * floor(C(m + 2,2) / 3)) / (1 - x^3)^floor(C(m + 2,2) / 3)).

Links

Crossrefs

Cf. A050531, A058389, A058407.

Formula

G.f.: 1/6*(1/(1-x)^15+3/(1-x)^3/(1-x^2)^6+2/(1-x^3)^5).

A058409 Number of 4 X n nonnegative integer matrices with all column sums 3, up to row and column permutation.

Original entry on oeis.org

1, 3, 18, 92, 458, 1982, 7928, 28592, 95138, 292993, 845027, 2295322, 5915631, 14535676, 34224682, 77510148, 169459010, 358698558, 737106306, 1473867060, 2873564862, 5472731212, 10198198452, 18621343624, 33361303957, 58713103696
Offset: 0

Views

Author

Vladeta Jovovic, Nov 25 2000

Keywords

Links

Crossrefs

Cf. A050532, A058390, A058407, A058408, A058410.

Formula

G.f.: 1 / 24*(1 / (1 - x)^20 + 6 / (1 - x)^6 / (1 - x^2)^7 + 3 / (1 - x^2)^10 + 8 / (1 - x)^2 / (1 - x^3)^6 + 6 / (1 - x^4)^5).

Extensions

More terms from Max Alekseyev, Jun 21 2011

A058410 Number of 4 X n nonnegative integer matrices with all column sums 4, up to row and column permutation.

Original entry on oeis.org

1, 5, 45, 407, 3411, 25142, 163711, 947909, 4949257, 23579022, 103592423, 423435205, 1622413728, 5864055622, 20102107500, 65660463140, 205176581382, 615506305973, 1778086106680, 4959845850882, 13391444267162, 35072585737475, 89275252614236, 221246652070184
Offset: 0

Views

Author

Vladeta Jovovic, Nov 25 2000

Keywords

Links

Crossrefs

Cf. A050532, A058390, A058407-A058409.

Formula

G.f.: 1 / 24*(1 / (1 - x)^35 + 6 / (1 - x)^9 / (1 - x^2)^13 + 3 / (1 - x)^3 / (1 - x^2)^16 + 8 / (1 - x)^2 / (1 - x^3)^11 + 6 / (1 - x) / (1 - x^2) / (1 - x^4)^8).

Extensions

More terms from Sean A. Irvine, Aug 05 2022

A058194 Number of n-rowed matrices with entries {0,1,2,3} and all row sums 3, up to row and column permutation.

Original entry on oeis.org

1, 3, 21, 162, 1636, 19977, 298416, 5300296, 110219750, 2639842989, 71859429837, 2198244062193, 74860247277672, 2815351714711122, 116130005180284423, 5222901881792429337, 254791333526874348652, 13420798291405599027605, 760201936044714899316798, 46137860613934391781325337, 2990483661567310913388458734
Offset: 0

Views

Author

Vladeta Jovovic, Nov 27 2000

Keywords

Crossrefs

Row n=3 of A331485.
Cf. A007717, A058407, A058409, A050913.

Programs

Extensions

a(11)-a(20) from Andrew Howroyd, Sep 06 2018
Showing 1-5 of 5 results.

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