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A122789
The (1,4)-entry in the matrix M^n, where M is the 4 X 4 matrix {{0, -1, -1, 1}, {1, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1 }}.
1
0, 1, 1, 0, 0, 1, 2, 2, 2, 3, 5, 7, 9, 12, 17, 24, 33, 45, 62, 86, 119, 164, 226, 312, 431, 595, 821, 1133, 1564, 2159, 2980, 4113, 5677, 7836, 10816, 14929, 20606, 28442, 39258, 54187, 74793, 103235, 142493, 196680, 271473, 374708, 517201, 713881, 985354
OFFSET
0,7
FORMULA
a(n)=a(n-1)+a(n-4); a(0)=0, a(1)=a(2)=1, a(3)=0 (follows from the minimal polynomial x^4 -x^3-1 of the matrix M).
G.f.: x(1+x)(1-x)/(1-x-x^4). a(n+1)= A003269(n)-A003269(n-2). - R. J. Mathar, Nov 25 2008
MAPLE
a[0]:=0: a[1]:=1: a[2]:=1: a[3]:=0: for n from 4 to 50 do a[n]:=a[n-1]+a[n-4] od: seq(a[n], n=0..50);
MATHEMATICA
M = {{0, -1, -1, 1}, {1, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1 }}; v[1] = {0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
CROSSREFS
Sequence in context: A100142 A296103 A247907 * A291294 A014208 A243358
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Nov 07 2006
Offset corrected to match data by Robert Israel, Jul 11 2014
STATUS
approved