OFFSET
1,8
LINKS
Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.
FORMULA
G.f.: -(2*x-1)*(x+1)*(x^2-x-1)/(-1+x^5-3*x^4-3*x^3+4*x^2+x). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
MAPLE
a[1]:=1: a[2]:=1: a[3]:=1: a[4]:=1: a[5]:=1: for n from 6 to 37 do a[n]:=a[n-1]+4*a[n-2]-3*a[n-3]-3*a[n-4]+a[n-5] od: seq(a[n], n=1..37);
MATHEMATICA
M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, -3, -3, 4, 1}}; v[1] = {1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
nxt[{a_, b_, c_, d_, e_}]:={b, c, d, e, e+4d-3c-3b+a}; NestList[nxt, {1, 1, 1, 1, 1}, 50][[;; , 1]] (* Harvey P. Dale, Aug 02 2024 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 20 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 08 2006
STATUS
approved