OFFSET
0,4
LINKS
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
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