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Search: id:A123943
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| A123943 |
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The (1,5)-entry in the 5 X 5 matrix M^n, where M={{5, 3, 2, 1, 1}, {3, 2, 1, 1, 0}, {2, 1, 1, 0, 0}, {1, 1, 0, 0, 0}, {1, 0, 0, 0, 0}} (n>=0). |
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+0
1
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| 0, 1, 5, 40, 315, 2490, 19681, 155563, 1229604, 9719061, 76821600, 607214857, 4799560053, 37936780428, 299860673343, 2370164848026, 18734305316497, 148080078051971, 1170457572108040, 9251554605638681, 73126326541645648
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OFFSET
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0,3
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REFERENCES
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See A123942 for references.
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FORMULA
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a(n)=8a(n-1)-6a(n-3)+a(n-5) for n>=5 (follows from the minimal polynomial of the matrix M).
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MAPLE
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with(linalg): M[1]:=matrix(5, 5, [5, 3, 2, 1, 1, 3, 2, 1, 1, 0, 2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]): for n from 2 to 22 do M[n]:=multiply(M[1], M[n-1]) od: 0, seq(M[n][1, 5], n=1..22);
a[0]:=0: a[1]:=1: a[2]:=5: a[3]:=40: a[4]:=315: for n from 5 to 22 do a[n]:=8*a[n-1]-6*a[n-3]+a[n-5] od: seq(a[n], n=0..22);
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MATHEMATICA
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M = {{5, 3, 2, 1, 1}, {3, 2, 1, 1, 0}, {2, 1, 1, 0, 0}, {1, 1, 0, 0, 0}, {1, 0, 0, 0, 0}}; v[1] = {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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Cf. A122099, A122100.
Sequence in context: A144069 A073505 A145841 this_sequence A067412 A078846 A027259
Adjacent sequences: A123940 A123941 A123942 this_sequence A123944 A123945 A123946
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Oct 25 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006
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