A052282 - OEIS

%I #24 Apr 04 2020 17:42:34

%S 1,1,3,5,9,13,22,30,45,61,85,111,149,189,244,304,381,465,571,685,825,

%T 977,1158,1354,1585,1833,2121,2431,2785,3165,3596,4056,4573,5125,5739,

%U 6393,7117,7885,8730,9626,10605,11641,12769,13959,15249,16609,18076,19620

%N Number of 3 X 3 stochastic matrices under row and column permutations.

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

%H Alois P. Heinz, <a href="/A052282/b052282.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-3,-1,1,3,-1,-2,1).

%F 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

%e There are 5 nonisomorphic 3 X 3 matrices with row and column sums 3:

%e [0 0 3] [0 0 3] [0 1 2] [0 1 2] [1 1 1]

%e [0 3 0] [1 2 0] [1 1 1] [1 2 0] [1 1 1]

%e [3 0 0] [2 1 0] [2 1 0] [2 0 1] [1 1 1]

%p 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

%t 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 *)

%Y Row n=3 of A333733.

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

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Feb 06 2000