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A107389 Expansion of x*(1-6*x+7*x^2)/( (1-x)*(1+x)*(1-5*x+x^2)). 2
0, 1, -1, 2, 5, 31, 144, 697, 3335, 15986, 76589, 366967, 1758240, 8424241, 40362959, 193390562, 926589845, 4439558671, 21271203504, 101916458857, 488311090775, 2339638995026, 11209883884349, 53709780426727, 257339018249280, 1232985310819681, 5907587535849119 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n)-a(n-2) = A030221(n-3), n>2. - R. J. Mathar, Dec 17 2017
MATHEMATICA
m = 5 M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, - m) Expand[Det[M - x*IdentityMatrix[4]]] (*-1 - 5 x + 5 x^3 + x^4*) NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M . v[n - 1] digits = 50; aa = Table[Abs[v[n][[1]], {n, 1, digits}]
Clear[M, m, v, aa] (*A107389*)m = 5; M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, m, 0, - m}}; Expand[Det[M - x*IdentityMatrix[4]]] ; NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] ; v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M . v[n - 1]; digits = 50; aa = Table[Abs[v[n][[1]]], {n, 1, digits}]
LinearRecurrence[{5, 0, -5, 1}, {0, 1, -1, 2}, 30] (* Harvey P. Dale, Sep 17 2020 *)
PROG
(PARI) concat(0, Vec((1-6*x+7*x^2)/(1-x)/(1+x)/(1-5*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Jan 25 2012
CROSSREFS
Sequence in context: A215168 A370830 A266478 * A261750 A189559 A077483
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, May 24 2005, corrected Sep 04 2008
EXTENSIONS
Irregular sign at a(2) switched by R. J. Mathar, Jan 24 2012
STATUS
approved

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Last modified June 20 20:53 EDT 2024. Contains 373532 sequences. (Running on oeis4.)