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
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 06 2000
STATUS
approved