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Search: id:A122265
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| A122265 |
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The (1,10)-entry of the matrix M^n, where M is the 10 X 10 matrix {{0,1,0,0,0, 0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0}, {0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,1,0,0},{0,0,0,0,0, 0,0,0,1,0},{0,0,0,0,0,0,0,0,0,1},{1,1,1,1,1,1,1,1,1,1}}. |
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+0
1
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| 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, 8172, 16336, 32656, 65280, 130496, 260864, 521472, 1042432, 2083841, 4165637, 8327186, 16646200, 33276064, 66519472, 132973664, 265816832, 531372800, 1062224128
(list; graph; listen)
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OFFSET
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0,12
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FORMULA
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a(n)=sum(a(n-j),j=1..10) for n>=10; a(n)=0 for 0<=n<=8, a(9)=1 (follows from the minimal polynomial of M; a Maple program based on this recurrence relation is much slower than the given Maple program, based on the definition).
G.f.:-x^9/(-1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
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MAPLE
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with(linalg): p:=-1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9+x^10: M[1]:=transpose(companion(p, x)): for n from 2 to 40 do M[n]:=multiply(M[n-1], M[1]) od: seq(M[n][1, 10], n=1..40);
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}}; v[1] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Floor[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
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Cf. A000322, A001591, A001592, A079262.
Sequence in context: A051535 A008862 A145116 this_sequence A113010 A056767 A008863
Adjacent sequences: A122262 A122263 A122264 this_sequence A122266 A122267 A122268
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula and Gary Adamson (qntmpkt(AT)yahoo.com), Oct 18 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2006
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