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Search: id:A107293
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| A107293 |
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The (1,1)-entry of the matrix M^n, where M is the 5 X 5 matrix [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,-1,1,1]]. |
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+0
4
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| 0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 6, 9, 13, 19, 27, 39, 56, 81, 117, 169, 244, 352, 508, 733, 1058, 1527, 2204, 3181, 4591, 6626, 9563, 13802, 19920, 28750, 41494, 59887, 86433, 124746, 180042, 259849, 375032, 541272, 781201, 1127483, 1627261, 2348575
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OFFSET
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0,7
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COMMENT
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Also the (1,2)-entries of M^n (n=1,2,...).
Characteristic polynomial of the matrix M is x^5-x^4-x^3+x^2-1.
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FORMULA
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Recurrence relation: a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-5) for n>=5; a(0)=a(1)=a(2)=a(3)=0,a(4)=1.
O.g.f: -x^4/(-1+x+x^2-x^3+x^5) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 02 2007
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MAPLE
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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);
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MATHEMATICA
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M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 0, -1, 1, 1}} ones = Table[MatrixPower[M, i][[1, 1]], {i, 1, 50}]
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CROSSREFS
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Adjacent sequences: A107290 A107291 A107292 this_sequence A107294 A107295 A107296
Sequence in context: A035561 A068106 A005856 this_sequence A107379 A001611 A039829
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 08 2005
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EXTENSIONS
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Edited by njas, May 12 2006
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