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Search: id:A094287
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| A094287 |
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Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 7 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 1. |
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+0
1
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| 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15510, 41822, 113531, 309937, 850118, 2340918, 6466953, 17913087, 49726649, 138287113, 385126811, 1073832695, 2996974774, 8370739326, 23394528640, 65415732100, 182989086965
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OFFSET
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1,2
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COMMENT
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In general a(n)=2/m*Sum_{k=1..m} Sin(Pi*k/m)^2(1+2Cos(Pi*k/m))^n counts the (s(0), s(1), ..., s(n)) such that 0 < s(i) < m and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 1. Here is m=7.
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FORMULA
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a(n)=(2/7)*Sum_{k=1..6} Sin(Pi*k/7)^2(1+2Cos(Pi*k/7))^n
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MATHEMATICA
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f[n_] := FullSimplify[ TrigToExp[(2/7)*Sum[ Sin[Pi*k/7]^2(1 + 2Cos[Pi*k/7])^n, {k, 1, 6}]]]; Table[ f[n], {n, 28}] (from Robert G. Wilson v Jun 18 2004)
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CROSSREFS
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Sequence in context: A051529 A005207 A094286 this_sequence A094288 A086246 A001006
Adjacent sequences: A094284 A094285 A094286 this_sequence A094288 A094289 A094290
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KEYWORD
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easy,nonn
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AUTHOR
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Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
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