A107389 Expansion of x*(1-6*x+7*x^2)/( (1-x)*(1+x)*(1-5*x+x^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

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (5,0,-5,1).

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

Adjacent sequences: A107386 A107387 A107388 * A107390 A107391 A107392

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