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Search: id:A094834
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| A094834 |
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Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 9 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = 3, s(2n+1) = 6. |
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+0
1
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| 1, 5, 21, 82, 308, 1131, 4096, 14705, 52497, 186733, 662630, 2347680, 8309143, 29388368, 103895601, 367187437, 1297452581, 4583924154, 16193659132, 57204089987, 202065531888, 713750040577, 2521114546457, 8905002445437
(list; graph; listen)
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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(r,1,m-1,Sin(r*j*Pi/m)Sin(r*k*Pi/m)(2Cos(r*Pi/m))^(2n+1)) counts (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < m and |s(i)-s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = j, s(2n+1) = k.
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FORMULA
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a(n)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/3)Sin(2*r*Pi/3)(2Cos(r*Pi/9))^(2n+1)) a(n)=6a(n-1)-9a(n-2)+a(n-3) G.f.: x(-1+x)/(-1+6x-9x^2+x^3)
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CROSSREFS
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Adjacent sequences: A094831 A094832 A094833 this_sequence A094835 A094836 A094837
Sequence in context: A029870 A081038 A051196 this_sequence A026017 A132310 A083319
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KEYWORD
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nonn
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AUTHOR
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Herbert Kociemba (kociemba(AT)t-online.de), Jun 13 2004
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