A052281 -id:A052281 - cp's OEIS frontend

A058390 Number of 4 X 4 matrices with nonnegative integer entries and all row sums equal to n, up to row and column permutation.

1, 5, 53, 458, 3411, 19865, 95214, 383714, 1346183, 4202086, 11905966, 31061806, 75533056, 172800689, 374861365, 775978710, 1541027694, 2949003213, 5458806804, 9805626744, 17140511056

Offset: 0

Vladeta Jovovic, Nov 24 2000

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..1000
Vladeta Jovovic, Number of m x m nonnegative integer matrices with all row sums equal to n, up to row and column permutation.

Row 4 of A318951.

Cf. A002620, A058389, A058391, A058392, A001496, A052280, A052281.

(* See A318951 for RowSumMats *)
a[n_] := RowSumMats[4, 4, n];
a /@ Range[0, 20] (* Jean-François Alcover, Sep 15 2019, after Andrew Howroyd *)

\\ See A318951 for RowSumMats
a(n)=RowSumMats(4, 4, n); \\ Andrew Howroyd, Sep 05 2018

A052282 Number of 3 X 3 stochastic matrices under row and column permutations.

Original entry on oeis.org

1, 1, 3, 5, 9, 13, 22, 30, 45, 61, 85, 111, 149, 189, 244, 304, 381, 465, 571, 685, 825, 977, 1158, 1354, 1585, 1833, 2121, 2431, 2785, 3165, 3596, 4056, 4573, 5125, 5739, 6393, 7117, 7885, 8730, 9626, 10605, 11641, 12769, 13959, 15249, 16609, 18076, 19620

Offset: 0

Vladeta Jovovic, Feb 06 2000

nonn

Unreduced numerators in convergent to log(2) = lim[n->inf, a(n)/A000670(n+1)].

			There are 5 nonisomorphic 3 X 3 matrices with row and column sums 3:
[0 0 3] [0 0 3] [0 1 2] [0 1 2] [1 1 1]
[0 3 0] [1 2 0] [1 1 1] [1 2 0] [1 1 1]
[3 0 0] [2 1 0] [2 1 0] [2 0 1] [1 1 1]

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-3,-1,1,3,-1,-2,1).

Row n=3 of A333733.

Cf. A002817, A052280, A052281. Different from A001993.

a:= n -> (Matrix([[1, 0, 0, 1, 1, 3, 5, 9, 13]]). Matrix(9, (i,j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -3, -1, 1, 3, -1, -2, 1][i] else 0 fi)^n)[1,1]: seq(a(n), n=0..50);  # Alois P. Heinz, Jul 31 2008

LinearRecurrence[{2,1,-3,-1,1,3,-1,-2,1},{1,1,3,5,9,13,22,30,45},50] (* Harvey P. Dale, Mar 10 2018 *)

G.f.: (x^6-x^5+x^3-x+1)/((1-x)^5*(1+x)^2*(1+x+x^2)). - Ralf Stephan and Vladeta Jovovic, May 07 2004

A052280 Number of 4 X 4 stochastic matrices under row and column permutations.

Original entry on oeis.org

1, 1, 5, 12, 43, 106, 321, 787, 1960, 4354, 9386, 18790, 36362, 66789, 118936, 203840, 340195, 551192, 873343, 1351457, 2052221, 3056798, 4480565, 6462678, 9194098, 12902867, 17892986, 24524478, 33265476, 44666016, 59426834, 78364873, 102502765, 133024660, 171390035, 219278224

Offset: 0

Vladeta Jovovic, Feb 06 2000

nonn

			There are 5 nonisomorphic 4 X 4 matrices with row and column sums 2:
[0 0 0 2] [0 0 0 2] [0 0 0 2] [0 0 1 1] [0 0 1 1]
[0 0 2 0] [0 0 2 0] [0 1 1 0] [0 0 1 1] [0 1 0 1]
[0 2 0 0] [1 1 0 0] [1 0 1 0] [1 1 0 0] [1 0 1 0]
[2 0 0 0] [1 1 0 0] [1 1 0 0] [1 1 0 0] [1 1 0 0]

Row n=4 of A333733.

Cf. A001496, A052281, A052282.

Terms a(9) and beyond from Andrew Howroyd, Apr 04 2020

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A058390 Number of 4 X 4 matrices with nonnegative integer entries and all row sums equal to n, up to row and column permutation.

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A052282 Number of 3 X 3 stochastic matrices under row and column permutations.

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A052280 Number of 4 X 4 stochastic matrices under row and column permutations.

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