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

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

0,3

Comments

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

Links

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).

Formula

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

Example

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]

Maple

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

Mathematica

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 *)

Crossrefs

Row n=3 of A333733.

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

Sequence in context: A141325 A248604 A146905 * A001993 A284829 A153263

Adjacent sequences: A052279 A052280 A052281 * A052283 A052284 A052285

Keyword

nonn

Author

Vladeta Jovovic, Feb 06 2000

Status

approved