login
A052282
Number of 3 X 3 stochastic matrices under row and column permutations.
5
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)].
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
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 06 2000
STATUS
approved