A122605 Expansion of -x*(2*x - 1)*(2*x^2 - 1)*(x^3 + 2*x^2 - x - 1)/((x - 1)*(x^2 + x - 1)*(x^4 - 4*x^3 - 4*x^2 + x + 1)).

1, 0, 0, 0, 0, 0, 0, -1, -1, -7, -8, -35, -44, -154, -208, -637, -910, -2548, -3808, -9996, -15504, -38760, -62015, -149225, -245135, -572010, -961125, -2186886, -3746886, -8348172, -14547183, -31842580, -56309764, -121415344, -217478888, -462925232, -838520240, -1765205473, -3228800413

Offset

1,10

Links

Table of n, a(n) for n=1..39.

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 (1,6,-5,-10,6,4,-1).

Formula

a(0)=1, a(1)=a(2)=a(3)=a(4)=a(5)=a(6)=0; for n>6, a(n) = a(n-1) + 6*a(n-2) - 5*a(n-3) - 10*a(n-4) + 6*a(n-5) + 4*a(n-6) - a(n-7). - Harvey P. Dale, May 02 2011

G.f.: -x*(2*x-1)*(2*x^2-1)*(x^3+2*x^2-x-1)/((x-1)*(x^2+x-1)*(x^4-4*x^3-4*x^2+x+1)). - Colin Barker, Nov 08 2012

Mathematica

LinearRecurrence[{1, 6, -5, -10, 6, 4, -1}, {1, 0, 0, 0, 0, 0, 0}, 60] (* Harvey P. Dale, May 02 2011 *)

Crossrefs

Cf. A066170.

Sequence in context: A042875 A154745 A048064 * A037953 A296636 A041106

Adjacent sequences: A122602 A122603 A122604 * A122606 A122607 A122608

Keyword

sign,easy

Author

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

Extensions

Edited by N. J. A. Sloane, Feb 11 2007

Definition changed using Barker's g.f. by Bruno Berselli, Sep 19 2017

Status

approved