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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 May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)