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A008764 Number of 3 X 3 symmetric stochastic matrices under row and column permutations. 0
1, 1, 2, 4, 6, 8, 12, 16, 21, 27, 34, 42, 52, 62, 74, 88, 103, 119, 138, 158, 180, 204, 230, 258, 289, 321, 356, 394, 434, 476, 522, 570, 621, 675, 732, 792, 856, 922, 992, 1066, 1143, 1223, 1308, 1396, 1488, 1584, 1684, 1788, 1897, 2009, 2126, 2248, 2374, 2504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..53.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-1,-1,1,-1,2,-1).

FORMULA

Expansion of (1+x^3)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4) = (1-x+x^2)/( (1+x)*(1+x+x^2)*(1+x^2)*(1-x)^4).

a(n) = A008762(n) - A008762(n-1) + A008762(n-2). - R. J. Mathar, Aug 06 2013

EXAMPLE

There are 6 nonisomorphic symmetric 3 X 3 matrices with row and column sums 4:

[0 0 4] [0 1 3] [0 1 3] [0 2 2] [0 2 2] [1 1 2]

[0 4 0] [1 2 1] [1 3 0] [2 0 2] [2 1 1] [1 2 1]

[4 0 0] [3 1 0] [3 0 1] [2 2 0] [2 1 1] [2 1 1]

CROSSREFS

Cf. A019298.

Sequence in context: A117146 A061553 A138934 * A228354 A065386 A048951

Adjacent sequences:  A008761 A008762 A008763 * A008765 A008766 A008767

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better description and more terms from Vladeta Jovovic, Feb 06 2000

STATUS

approved

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Last modified March 27 08:23 EDT 2017. Contains 284146 sequences.