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
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).
Programs
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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
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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);
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Mathematica
LinearRecurrence[{1,1,-1,0,1}, {0,0,0,0,1}, 50] (* G. C. Greubel, Nov 03 2018 *) -
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
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
Extensions
Edited by N. J. A. Sloane, May 12 2006
Comments