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A107332 The (1,3)-entry of the matrix M^n, where M is the 5x5 matrix [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,-1,1,1]]. 1
0, 1, 0, 0, -1, -1, -1, -1, -1, -2, -3, -5, -7, -10, -14, -20, -29, -42, -61, -88, -127, -183, -264, -381, -550, -794, -1146, -1654, -2387, -3445, -4972, -7176, -10357, -14948, -21574, -31137, -44939, -64859, -93609, -135103, -194990, -281423, -406169, -586211, -846060, -1221092, -1762364 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Characteristic polynomial of the matrix M is x^5-x^4-x^3+x^2-1.

LINKS

Table of n, a(n) for n=1..47.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1).

FORMULA

Recurrence relation: a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-5) for n>=5.

O.g.f.: x^2*(-1+x+x^2)/(-1+x+x^2-x^3+x^5). - R. J. Mathar, Dec 02 2007

a(n) = A107293(n+2)-A107293(n+1)-A107293(n). - R. J. Mathar, Dec 17 2017

MAPLE

a[0]:=0:a[1]:=1:a[2]:=0:a[3]:=0:a[4]:=-1: for n from 5 to 46 do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-5] od: seq(a[n], n=0..46);

MATHEMATICA

M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 0, -1, 1, 1}} threes = Table[Abs[MatrixPower[M, i][[1, 3]]], {i, 1, 50}]

LinearRecurrence[{1, 1, -1, 0, 1}, {0, 1, 0, 0, -1}, 50] (* Harvey P. Dale, Oct 11 2015 *)

CROSSREFS

Sequence in context: A321728 A214077 A094984 * A002062 A005688 A241550

Adjacent sequences:  A107329 A107330 A107331 * A107333 A107334 A107335

KEYWORD

sign,easy

AUTHOR

Roger L. Bagula, Jun 08 2005

EXTENSIONS

Edited by N. J. A. Sloane, May 13 2006

STATUS

approved

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)