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

Author

Vladeta Jovovic, Feb 06 2000

Keywords

• nonn

Comments

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

Examples

			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]
		

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).

Crossrefs

Row n=3 of A333733.

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

Programs

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 *)

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