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A135991 Expansion of x^3*(x-1)^2*(x+1) / (x^6-3*x^5+3*x^4-x+1) 0
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 (list; graph; refs; listen; history; text; internal format)
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 to sequences with 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: A034389 A084196 A127913 * A102003 A176314 A004587

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

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Last modified September 1 10:14 EDT 2014. Contains 246291 sequences.