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Search: id:A117761
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| A117761 |
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First entry of the vector (M^n)w, where M is the 7x7 matrix [[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1],[1,0,1,0,1,0,1]] and w is the column vector [0,1,1,2,3,5,8]. |
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1
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| 0, 1, 1, 2, 3, 5, 8, 12, 20, 32, 51, 82, 131, 210, 336, 538, 862, 1380, 2210, 3539, 5667, 9075, 14532, 23271, 37265, 59674, 95559, 153023, 245043, 392399, 628367, 1006234, 1611330, 2580299, 4131955, 6616695, 10595627, 16967279, 27170507, 43509419
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OFFSET
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0,4
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MAPLE
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with(linalg): M:=matrix(7, 7, [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]): w[0]:=matrix(7, 1, [0, 1, 1, 2, 3, 5, 8]): for n from 1 to 40 do w[n]:=multiply(M, w[n-1]) od: seq(w[n][1, 1], n=0..40);
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 0, 0 }, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1}, {1, 0, 1, 0, 1, 0, 1}} w[1] = {0, 1, 1, 2, 3, 5, 8} w[n_] := w[n] = M.w[n - 1] Table[w[n][[1]], {n, 1, 25}] Det[M - x*IdentityMatrix[7]]
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CROSSREFS
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Sequence in context: A060961 A013984 A107479 this_sequence A018149 A118604 A072123
Adjacent sequences: A117758 A117759 A117760 this_sequence A117762 A117763 A117764
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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), Apr 14 2006
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EXTENSIONS
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Edited by njas, Apr 30 2006
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