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Search: id:A094297
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| A094297 |
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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) = 2. |
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+0
2
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| 1, 3, 7, 18, 46, 120, 316, 840, 2248, 6048, 16336, 44256, 120160, 326784, 889792, 2424960, 6613120, 18043392, 49247488, 134450688, 367134208, 1002645504, 2738510848, 7480215552, 20433258496, 55818559488, 152486858752
(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,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
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a(n)=(1/3)*Sum(k, 1, 5, Sin(Pi*k/3)^2(1+2Cos(Pi*k/6))^n) or a(n)=( 2^n+(1-Sqrt(3))^n + (1+Sqrt(3))^n )/4
(a(n)) seems to be given by tesseq(- 2'i + 2'j + 2'k - 2i' + 2j' + 2k' - 2'ii' + 2'jj' - 'kk' - 2.5'ik' - 1.5'jk' - 2.5'ki' - 1.5'kj' - e) (disregarding signs) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 17 2004
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CROSSREFS
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First differences of A038508.
Adjacent sequences: A094294 A094295 A094296 this_sequence A094298 A094299 A094300
Sequence in context: A078058 A052960 A059512 this_sequence A026107 A027969 A027971
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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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