A122173 Expansion of -x * (x^5+x^4-15*x^3+19*x^2-8*x+1) / (x^6-12*x^5+34*x^4-30*x^3+6*x^2+3*x-1).

1, -5, 10, -45, 110, -421, 1148, -4037, 11697, -39250, 117736, -384657, 1177235, -3787218, 11727187, -37389217, 116571621, -369712938, 1157315631, -3659226205, 11481436216, -36237006073, 113856243558, -358967583724, 1128781753801, -3556642214960, 11189229179710

Offset: 1

Author

Gary W. Adamson and Roger L. Bagula, Oct 17 2006

Keywords

• sign
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..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 (3,6,-30,34,-12,1).

Crossrefs

Cf. A046854. Cf. A046854. Cf. A007700, A059455. Cf. A065941.

Programs

Mathematica

M = {{0, -1, -1, -1, -1, -1}, {-1, 0, -1, -1, -1, 0}, {-1, -1, 0, -1, 0, 0}, {-1, -1, -1, 1, 0, 0}, {-1, -1, 0, 0, 1, 0}, {-1, 0, 0, 0, 0, 1}}; v[1] = {1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Floor[v[n][[1]]], {n, 1, 50}]
LinearRecurrence[{3,6,-30,34,-12,1},{1,-5,10,-45,110,-421},30] (* Harvey P. Dale, Mar 16 2025 *)

Formula

G.f.: -x*(x^5+x^4-15*x^3+19*x^2-8*x+1)/(x^6-12*x^5+34*x^4-30*x^3+6*x^2+3*x-1). [Colin Barker, Oct 19 2012]

Extensions

Sequence edited by Joerg Arndt, Colin Barker, Bruno Berselli, Oct 19 2012