A122582 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 2*a(n - 4) + a(n - 5).

1, 1, 1, 1, 1, -1, -3, -1, 3, 5, 3, -5, -13, -7, 13, 27, 15, -25, -61, -37, 57, 135, 81, -119, -297, -191, 257, 661, 431, -549, -1455, -991, 1169, 3225, 2257, -2497, -7115, -5145, 5299, 15725, 11715, -11261, -34709, -26623, 23829, 76603, 60479, -50361, -168997, -137173, 106105, 372655, 310905, -222951

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

Cf. A122581, A122583, A122584.

Sequence in context: A005474 A012264 A063198 * A173039 A016471 A324294

Adjacent sequences: A122579 A122580 A122581 * A122583 A122584 A122585

Keyword

sign

Author

Roger L. Bagula, Sep 19 2006

Extensions

Edited by N. J. A. Sloane, Oct 01 2006, Jan 01 2007

Status

approved