A122608 a(1) = 1; a(2) = 1; a(3) = 1; a(4) = 1; a(5) = 1; a(n) = a(n-1)+4a(n-2)-3a(n-3)-3a(n-4)+a(n-5) for n >= 6.

1, 1, 1, 1, 1, 0, -1, -6, -12, -32, -59, -134, -244, -519, -948, -1949, -3586, -7225, -13397, -26640, -49744, -98024, -184114, -360455, -680247, -1325397, -2510702, -4874298, -9260629, -17929771, -34142684, -65967689, -125841523, -242755543, -463720287, -893457507, -1708515146

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 20 2006

Keywords

• sign

Links

• Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31.

Crossrefs

Cf. A066170.

Programs

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 *)

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]

Extensions

Edited by N. J. A. Sloane, Oct 08 2006