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Search: id:A122789
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| A122789 |
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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 }}. |
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+0
1
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| 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; listen)
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OFFSET
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1,7
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FORMULA
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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). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 25 2008]
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MAPLE
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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);
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A077018 A007918 A126111 this_sequence A014208 A059690 A121256
Adjacent sequences: A122786 A122787 A122788 this_sequence A122790 A122791 A122792
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KEYWORD
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nonn
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 20 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 07 2006
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