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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 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

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