A121798 - OEIS

%I #10 Jul 31 2015 20:35:16

%S 0,28,408,1502,7821,31911,145162,616196,2706385,11640499,50598522,

%T 218517332,946752849,4093542243,17716803778,76627964684,331523693857,

%U 1434000301795,6203258085066,26832402306020,116067057052689

%N a(n)= 4*a(n-1) +13*a(n-2) -44*a(n-3) -57*a(n-4) +120*a(n-5) +63*a(n-6) -56*a(n-7) +6*a(n-8).

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4, 13, -44, -57, 120, 63, -56, 6).

%F G.f.: x^2*(-28-296*x+494*x^2+2259*x^3-649*x^4-1829*x^5+281*x^6)/( (3*x-1) * (1+x) * (x^2-2*x-1) * (2*x^4-16*x^3+5*x^2+4*x-1)). [Oct 14 2009]

%t M = {{0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0}, {1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1}, { 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 01}, {0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 11}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[12]] Factor[%] aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[12]] == 0, x][[n]], {n, 1, 12}]

%t LinearRecurrence[{4,13,-44,-57,120,63,-56,6},{0,28,408,1502,7821,31911,145162,616196},30] (* _Harvey P. Dale_, Feb 29 2012 *)

%K nonn

%O 1,2

%A _Roger L. Bagula_, Aug 26 2006

%E Definition replaced by recurrence - The Assoc. Editors of the OEIS, Oct 14 2009