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A052282 Number of 3 X 3 stochastic matrices under row and column permutations. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified February 19 22:38 EST 2019. Contains 320328 sequences. (Running on oeis4.)