OFFSET
0,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.
Index entries for linear recurrences with constant coefficients, signature (2,5,-13,7,-1).
FORMULA
a(n) = 2*a(n-1)+5*a(n-2)-13*a(n-3)+7*a(n-4)-a(n-5); a(0)=1, a(1)=-4, a(2)=6, a(3)=-24, a(4)=41 (follows from the minimal polynomial x^5-2*x^4-5*x^3+13*x^2-7*x+1 of the matrix M).
G.f.: (1-3*x^3+9*x^2-6*x)/(1+x^5-7*x^4+13*x^3-5*x^2-2*x). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
MAPLE
with(linalg): M[1]:=matrix(5, 5, [0, -1, -1, -1, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, 0, -1, -1, 0, 1, 0, -1, 0, 0, 0, 1]): for n from 2 to 30 do M[n]:=multiply(M[n-1], M[1]) od: 1, seq(M[n][1, 1]+M[n][1, 2]+M[n][1, 3]+M[n][1, 4]+M[n][1, 5], n=1..30);
MATHEMATICA
M = {{0, -1, -1, -1, -1}, {-1, 0, -1, -1, 0}, {-1, -1, 0, 0, 0}, {-1, -1, 0, 1, 0}, {-1, 0, 0, 0, 1}}; v[1] = {1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 25}]
PROG
(PARI) a(n) = my(m=[0, -1, -1, -1, -1; -1, 0, -1, -1, 0; -1, -1, 0, 0, 0; -1, -1, 0, 1, 0; -1, 0, 0, 0, 1]); vecsum((m^n)[1, ]); \\ Michel Marcus, Jun 21 2017
CROSSREFS
KEYWORD
sign,easy,less
AUTHOR
Gary W. Adamson and Roger L. Bagula, Oct 17 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 29 2006
STATUS
approved