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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Robert Israel, Table of n, a(n) for n = 0..3570

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1).

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: A126111 A296103 A247907 * A291294 A014208 A243358

Adjacent sequences:  A122786 A122787 A122788 * A122790 A122791 A122792

KEYWORD

nonn

AUTHOR

Gary W. Adamson and Roger L. Bagula, Oct 20 2006

EXTENSIONS

Edited by N. J. A. Sloane, Nov 07 2006

Offset corrected to match data by Robert Israel, Jul 11 2014

STATUS

approved

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Last modified July 12 22:46 EDT 2020. Contains 335669 sequences. (Running on oeis4.)