A107293 The (1,1)-entry of the matrix M^n, where M is the 5 X 5 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]].

0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 6, 9, 13, 19, 27, 39, 56, 81, 117, 169, 244, 352, 508, 733, 1058, 1527, 2204, 3181, 4591, 6626, 9563, 13802, 19920, 28750, 41494, 59887, 86433, 124746, 180042, 259849, 375032, 541272, 781201, 1127483, 1627261, 2348575

Offset

0,7

Comments

Also the (1,2)-entries of M^n (n >= 1).

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

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

O.g.f: x^4/(1 - x - x^2 + x^3 - x^5). - R. J. Mathar, Dec 02 2007

Maple

a[0]:=0:a[1]:=0:a[2]:=0:a[3]:=0:a[4]:=1: for n from 5 to 45 do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-5] od: seq(a[n], n=0..45);

Mathematica

LinearRecurrence[{1, 1, -1, 0, 1}, {0, 0, 0, 0, 1}, 50] (* G. C. Greubel, Nov 03 2018 *)

Prog

(PARI) m=50; v=concat([0, 0, 0, 0, 1], vector(m-5)); for(n=6, m, v[n] = v[n-1] +v[n-2] -v[n-3] +v[n-5]); v \\ G. C. Greubel, Nov 03 2018
(Magma) I:=[0, 0, 0, 0, 1]; [n le 5 select I[n] else Self(n-1) +Self(n-2) -Self(n-3) + Self(n-5): n in [1..50]]; // G. C. Greubel, Nov 03 2018

Crossrefs

Sequence in context: A351973 A212264 A174650 * A329693 A329976 A329703

Adjacent sequences: A107290 A107291 A107292 * A107294 A107295 A107296

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 08 2005

Extensions

Edited by N. J. A. Sloane, May 12 2006

Status

approved