

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]].


19



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
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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(n1) + a(n2)  a(n3) + a(n5) 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[n1]+a[n2]a[n3]+a[n5] 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(m5)); for(n=6, m, v[n] = v[n1] +v[n2] v[n3] +v[n5]); v \\ G. C. Greubel, Nov 03 2018
(Magma) I:=[0, 0, 0, 0, 1]; [n le 5 select I[n] else Self(n1) +Self(n2) Self(n3) + Self(n5): 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



