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A122582 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 2*a(n - 4) + a(n - 5). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

This recursion is inspired by Ulam's early experiments in derivative recursions.

LINKS

Table of n, a(n) for n=1..54.

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[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 1; a[n_] := a[n] = a[n - 1] - 2*a[n - 2] + a[n - 3] + (-2*a[n - 4] + a[n - 5]); Table[a[n], {n, 0, 30}]

Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{1, -2, 1, -2, 1}, #]}]&, {1, 1, 1, 1, 1}, 60]][[1]]  (* Harvey P. Dale, Mar 21 2011 *)

CROSSREFS

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

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)