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A094306
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Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 2, s(n) = 4.
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1
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1, 3, 10, 30, 88, 252, 712, 1992, 5536, 15312, 42208, 116064, 318592, 873408, 2392192, 6547584, 17912320, 48985344, 133926400, 366085632, 1000548352, 2734316544, 7471826944, 20416481280, 55785005056, 152419749888
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| In general a(n,m,j,k)=2/m*Sum_{r=1..m-1} Sin(j*r*Pi/m)Sin(k*r*Pi/m)(1+2Cos(Pi*r/m))^n) is the number of (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) = j, s(n) = k.
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FORMULA
| a(n)=( (1-Sqrt(3))^n + (1+Sqrt(3))^n -2^n )/4; a(n)=(1/3)*Sum_{k=1..5} Sin(Pi*k/3)Sin(2Pi*k/3)(1+2Cos(Pi*k/6))^n
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MATHEMATICA
| f[n_] := FullSimplify[ TrigToExp[(1/3)Sum[ Sin[Pi*k/3] Sin[2Pi*k/3] (1 + 2Cos[Pi*k/6])^n, {k, 1, 5}]]]; Table[ f[n], {n, 2, 27}] (from Robert G. Wilson v Jun 18 2004)
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CROSSREFS
| Sequence in context: A092756 A027205 A026937 * A026109 A026327 A014531
Adjacent sequences: A094303 A094304 A094305 * A094307 A094308 A094309
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KEYWORD
| easy,nonn
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AUTHOR
| Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
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