A121798 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).

0, 28, 408, 1502, 7821, 31911, 145162, 616196, 2706385, 11640499, 50598522, 218517332, 946752849, 4093542243, 17716803778, 76627964684, 331523693857, 1434000301795, 6203258085066, 26832402306020, 116067057052689

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (4, 13, -44, -57, 120, 63, -56, 6).

Formula

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]

Mathematica

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

Crossrefs

Sequence in context: A010980 A022592 A323973 * A238600 A278009 A233333

Adjacent sequences: A121795 A121796 A121797 * A121799 A121800 A121801

Keyword

nonn

Author

Roger L. Bagula, Aug 26 2006

Extensions

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

Status

approved