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
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Jun 08 2005
EXTENSIONS
Edited by N. J. A. Sloane, May 12 2006
STATUS
approved