A122583 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 6*a(n - 4) + 3*a(n - 5).

1, 1, 1, 1, 1, -3, -7, -3, 5, 25, 45, -3, -107, -191, -175, 253, 1045, 1189, -171, -3547, -7527, -4603, 11497, 33945, 40869, -10487, -141071, -248407, -120131, 421141, 1227961, 1332777, -726439, -5051271, -8369959, -3306635, 16738977, 43110597, 41391949, -33360335, -183387403, -283721435

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,-6,3).

Formula

G.f.: x*(1 +2*x^2 +x^3 +7*x^4)/(1 -x +2*x^2 -x^3 +6*x^4 -3*x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

Maple

A122583:= proc(n) option remember; if n <= 5 then 1; else A122583(n-1) -2*A122583(n-2)+A122583(n-3)+3*(-2*A122583(n-4)+A122583(n-5)); fi; end: seq(A122583(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] -6*a[n-4] +3*a[n-5]];
Table[a[n], {n, 50}]

Prog

(Magma) [n le 5 select 1 else Self(n-1) -2*Self(n-2) +Self(n-3) -6*Self(n-4) +3*Self(n-5): n in [1..50]]; // G. C. Greubel, Nov 28 2021
(Sage)
@CachedFunction # a=A122583
def a(n): return 1 if (n<6) else a(n-1) -2*a(n-2) +a(n-3) -6*a(n-4) +3*a(n-5)
[a(n) for n in (1..50)] # G. C. Greubel, Nov 28 2021

Crossrefs

Cf. A122581, A122582, A122584.

Sequence in context: A096247 A337013 A362026 * A001265 A060443 A020810

Adjacent sequences: A122580 A122581 A122582 * A122584 A122585 A122586

Keyword

sign

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