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Search: id:A103999
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| A103999 |
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Square array T(M,N) read by antidiagonals: number of dimer tilings of a 2M x 2N Klein bottle. |
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+0
6
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| 1, 1, 1, 1, 6, 1, 1, 16, 34, 1, 1, 54, 196, 198, 1, 1, 196, 1666, 2704, 1154, 1, 1, 726, 16384, 64152, 37636, 6726, 1, 1, 2704, 171394, 1844164, 2549186, 524176, 39202, 1, 1, 10086, 1844164, 57523158, 220581904, 101757654, 7300804, 228486, 1, 1
(list; table; graph; listen)
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OFFSET
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0,5
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LINKS
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Author?, About Klein bottles
W. T. Lu and F. Y. Fu, Dimer statistics on the Moebius strip and the Klein bottle
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FORMULA
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T(M, N) = Prod[m=1..M, Prod[n=1..N, 4sin(Pi*(4n-1)/(4N))^2 + 4sin(Pi*(2m-1)/(2M))^2 ]].
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EXAMPLE
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1,1,1,1,1,1,1,
1,6,34,198,1154,6726,39202,
1,16,196,2704,37636,524176,7300804,
1,54,1666,64152,2549186,101757654,4064620168,
1,196,16384,1844164,220581904,26743369156,3252222705664,
1,726,171394,57523158,21050622914,7902001927776,2988827208115522,
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CROSSREFS
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Rows include A003499, A067902+2. Columns include A003500+2.
Cf. A099390, A103997.
Sequence in context: A086645 A109001 A119726 this_sequence A060972 A056941 A060187
Adjacent sequences: A103996 A103997 A103998 this_sequence A104000 A104001 A104002
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Feb 26 2005
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