OFFSET
1,7
COMMENTS
This recursion is inspired by Ulam's early experiments in derivative recursions.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,-2,1,-2,1).
FORMULA
G.f.: x*(1+2*x^2+x^3+3*x^4)/(1-x+2*x^2-x^3+2*x^4-x^5). - R. J. Mathar, May 12 2013
MATHEMATICA
a[n_]:= a[n]= If[n<6, 1, a[n-1] -2*a[n-2] +a[n-3] -2*a[n-4] +a[n-5]];
Table[a[n], {n, 60}]
Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{1, -2, 1, -2, 1}, #]}]&, {1, 1, 1, 1, 1}, 60]][[1]] (* Harvey P. Dale, Mar 21 2011 *)
PROG
(Magma) [n le 5 select 1 else Self(n-1) -2*Self(n-2) +Self(n-3) -2*Self(n-4) +Self(n-5): n in [1..50]]; // G. C. Greubel, Nov 28 2021
(Sage)
@CachedFunction # a=A122582
def a(n): return 1 if (n<6) else a(n-1) -2*a(n-2) +a(n-3) -2*a(n-4) +a(n-5)
[a(n) for n in (1..50)] # G. C. Greubel, Nov 28 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Roger L. Bagula, Sep 19 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 01 2006, Jan 01 2007
STATUS
approved