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A169766
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Number of closed knight's tour diagrams of a 3 X n chessboard that have "Bergholtian symmetry".
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2
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0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 48, 0, 152, 0, 352, 0, 1200, 0, 3752, 0, 12912, 0, 34768, 0, 122120, 0, 346128, 0, 1202240, 0, 3337424, 0, 11650864, 0, 32634960, 0, 113539392, 0, 316870592, 0, 1104442752, 0, 3086894528, 0, 10748713792, 0, 30023935744, 0
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OFFSET
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4,7
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COMMENTS
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When the board is rotated 180 degrees, the diagram remains the same, but the tour reverses direction.
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REFERENCES
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D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.
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LINKS
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FORMULA
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a(n) = 0 unless n mod 2 = 0.
Generating function: (2*(2*z^10 - 8*z^14 + 24*z^16 - 76*z^18 + 32*z^20 + 288*z^22 - 716*z^24 + 792*z^26 - 336*z^28 - 2908*z^30 + 7896*z^32 - 1464*z^34 - 3432*z^36 + 7416*z^38 - 32616*z^40 - 11792*z^42 + 39888*z^44 + 35472*z^46 + 47968*z^48 + 35776*z^50 - 143424*z^52 - 197824*z^54 - 15552*z^56 - 11008*z^58 + 181376*z^60 + 269440*z^62 + 78080*z^64 + 53760*z^66 + 44288*z^68 - 48128*z^70 - 112640*z^72 - 124928*z^74 - 227328*z^76 - 155648*z^78 + 98304*z^80 + 147456*z^82 + 32768*z^84))/
(1 - 6*z^4 - 64*z^8 + 200*z^12 + 1000*z^16 - 3016*z^20 - 3488*z^24 + 24256*z^28 - 23776*z^32 - 104168*z^36 + 203408*z^40 + 184704*z^44 - 443392*z^48 - 14336*z^52 + 151296*z^56 - 145920*z^60 + 263424*z^64 - 317440*z^68 - 36864*z^72 + 966656*z^76 - 573440*z^80 - 131072*z^84)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms extracted from the g.f. by R. J. Mathar, Oct 09 2010
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STATUS
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approved
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