A122581 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 4*a(n - 4) + 2*a(n - 5).

1, 1, 1, 1, 1, -2, -5, -2, 4, 13, 19, -5, -50, -65, -20, 118, 283, 187, -311, -914, -1001, 334, 3040, 4405, 835, -8273, -17030, -11189, 20068, 60178, 60427, -29165, -192491, -274310, -39845, 553798, 1070812, 635629, -1341437, -3836765, -3693914, 2237287, 12425356, 16921054, 1409755, -36343973

Offset

1,6

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,-4,2).

Formula

G.f.: x*(1+2*x^2+x^3+5*x^4)/(1-x+2*x^2-x^3+4*x^4-2*x^5). - R. J. Mathar, Nov 18 2007

Maple

A122581:= proc(n) option remember; if n <= 5 then 1; else A122581(n-1) -2*A122581(n-2)+A122581(n-3)+2*(-2*A122581(n-4)+A122581(n-5)); fi; end: seq(A122581(n), n=1..50) ; # R. J. Mathar, Sep 18 2007

Mathematica

a[n_]:= a[n]= If[n<6, 1, a[n-1] -2*a[n-2] +a[n-3] -2*(2*a[n-4] -a[n-5])];
Table[a[n], {n, 50}]

Prog

(SageMath)
@CachedFunction # a=A122581
def a(n): return 1 if (n<6) else a(n-1) -2*a(n-2) +a(n-3) -4*a(n-4) +2*a(n-5)
[a(n) for n in (1..50)] # G. C. Greubel, Nov 28 2021
(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 2, -4, 1, -2, 1]^(n-1)*[1; 1; 1; 1; 1])[1, 1] \\ Charles R Greathouse IV, May 20 2026

Crossrefs

Cf. A122582, A122583, A122584.

Sequence in context: A275748 A375909 A216625 * A151871 A220247 A220319

Adjacent sequences: A122578 A122579 A122580 * A122582 A122583 A122584

Keyword

sign,easy

Author

Roger L. Bagula, Sep 19 2006

Extensions

Edited by N. J. A. Sloane, Oct 01 2006

More terms from R. J. Mathar, Sep 18 2007

Status

approved