OFFSET
1,2
LINKS
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
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