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Search: id:A122365
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| A122365 |
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The (1,6)-entry of the matrix M^n, where M is the 6 X 6 matrix {{1, 1, 1, 1, 1, 1},{1, 0, 0, 0, 1, 0},{1, 0, 0, 1, 0, 0},{1, 0, 1, 0, 0, 0},{1, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}}. |
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+0
1
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| 0, 1, 1, 6, 15, 53, 160, 517, 1621, 5150, 16267, 51513, 162944, 515673, 1631609, 5162966, 16336695, 51693645, 163571104, 517580093, 1637750957, 5182251182, 16397926099, 51887105969, 164183665152, 519517828081, 1643883210801
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OFFSET
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0,4
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FORMULA
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a(n)=2a(n-1)+5a(n-2)-3a(n-3)-4a(n-4)+a(n-5); a(0)=0, a(1)=1, a(2)=1,a(3)=6,a(4)=15 (follows from the minimal polynomial of M).
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MAPLE
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a[0]:=0: a[1]:=1: a[2]:=1: a[3]:=6: a[4]:=15: for n from 5 to 26 do a[n]:=2*a[n-1]+5*a[n-2]-3*a[n-3]-4*a[n-4]+a[n-5] od: seq(a[n], n=0..26);
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MATHEMATICA
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M = {{1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 1, 0}, {1, 0, 0, 1, 0, 0}, {1, 0, 1, 0, 0, 0}, {1, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}}; v[1] = {0, 0, 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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Adjacent sequences: A122362 A122363 A122364 this_sequence A122366 A122367 A122368
Sequence in context: A056423 A056347 A082009 this_sequence A119132 A073065 A093042
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KEYWORD
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nonn
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AUTHOR
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Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 19 2006
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EXTENSIONS
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Edited by njas, Oct 29 2006
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