%I #27 Sep 08 2022 08:45:18

%S 0,0,0,0,1,1,2,2,3,4,6,9,13,19,27,39,56,81,117,169,244,352,508,733,

%T 1058,1527,2204,3181,4591,6626,9563,13802,19920,28750,41494,59887,

%U 86433,124746,180042,259849,375032,541272,781201,1127483,1627261,2348575

%N 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]].

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

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

%H G. C. Greubel, <a href="/A107293/b107293.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,1).

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

%F O.g.f: x^4/(1 - x - x^2 + x^3 - x^5). - _R. J. Mathar_, Dec 02 2007

%p 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);

%t LinearRecurrence[{1,1,-1,0,1}, {0,0,0,0,1}, 50] (* _G. C. Greubel_, Nov 03 2018 *)

%o (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

%o (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

%K nonn,easy

%O 0,7

%A _Roger L. Bagula_, Jun 08 2005

%E Edited by _N. J. A. Sloane_, May 12 2006