|
%I #10 Mar 19 2017 13:57:00
%S 1,1,1,1,1,1,1,1,1,2,3,12,22,76,141,414,764,2024,3724,9232,16984,
%T 40240,74155,170086,314296,703663,1304538,2866813,5333562,11549771,
%U 21564748,46147004,86466720,183234616,344510288,724134585,1365974770,2851430605
%N Expansion of x*(x^3+3*x^2-1)*(5*x^4-5*x^2+1) / ( -1+x+8*x^2-7*x^3-21*x^4+15*x^5+20*x^6-10*x^7-5*x^8+x^9 )
%C Can be extracted from the top left element of the n-th power of the 9 X 9 matrix shown in the Mathematica program.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,8,-7,-21,15,20,-10,-5,1).
%t M = {{0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, -5, -10, 20, 15, -21, -7, 8, 1}}; v[1] = Table[1, {n, 0, 8}]; v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
%K nonn,less
%O 1,10
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 20 2006
|
