A135991 Expansion of x^3*(x-1)^2*(x+1) / (x^6-3*x^5+3*x^4-x+1).

0, 0, 1, 0, -1, 0, -3, 0, 2, -1, 9, 0, -3, 6, -26, 2, 2, -25, 74, -16, 10, 89, -210, 85, -67, -288, 599, -375, 291, 869, -1725, 1485, -1112, -2471, 5020, -5479, 4037, 6629, -14732, 19236, -14332, -16629, 43417, -65116, 50320, 37975, -127831, 214397, -175328

Offset

1,7

Comments

The ratio is "ringing" cyclic:

Table[N[a[[n]]/a[[n - 1]]], {n, 8, 100}]

The sequence alternates and is relatively low in value a little longer than other such sequences.

Links

Table of n, a(n) for n=1..49.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,-3,3,-1).

Formula

G.f.: x^3*(x-1)^2*(x+1) / (x^6-3*x^5+3*x^4-x+1). - Colin Barker, Feb 02 2013

Mathematica

Clear[v, m, n, M0, N0] v[0] = {0, 0, 1}; v[1] = {0, 1, 2}; M0 = {{0, 1, 0}, {0, 0, 1}, {1, 0, 1}}; N0 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}; v[n_] := v[n] = N0.v[n - 1] - M0.v[n - 2] a = Table[v[n][[1]], {n, 0, 100}]

Crossrefs

Sequence in context: A295041 A359710 A127913 * A331422 A279631 A102003

Adjacent sequences: A135988 A135989 A135990 * A135992 A135993 A135994

Keyword

sign,easy

Author

Roger L. Bagula, Mar 03 2008

Extensions

Better name by Colin Barker, Feb 02 2013

Status

approved