A122161 Expansion of x*(1 - 3*x + x^2) / (1 - x - 2*x^2 + x^3).

1, -2, 1, -4, 0, -9, -5, -23, -24, -65, -90, -196, -311, -613, -1039, -1954, -3419, -6288, -11172, -20329, -36385, -65871, -118312, -213669, -384422, -693448, -1248623, -2251097, -4054895, -7308466, -13167159, -23729196, -42755048, -77046281, -138827181, -250164695, -450772776

Offset: 1

Author

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

Keywords

• easy
• sign

Links

• P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-1).

Programs

Mathematica

M = {{0, -1, -1}, {-1, 0, 0}, {-1, 0, 1}}; v[1] = {1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]

PARI

Vec( x*(1 - 3*x + x^2) / (1 - x - 2*x^2 + x^3) + O(x^50)) \\ Michel Marcus, Sep 19 2017

Formula

a(n) = A006053(n+1) - 3*A006053(n) + A006053(n-1). - R. J. Mathar, Nov 07 2011