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Search: id:A075435
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| A075435 |
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T(n,k) = right- or upward-moving paths connecting opposite corners of a n*n chessboard, visiting the diagonal at k points between start and finish. |
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+0
2
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| 2, 6, 4, 20, 24, 8, 70, 116, 72, 16, 252, 520, 456, 192, 32, 924, 2248, 2496, 1504, 480, 64, 3432, 9520, 12624, 9728, 4480, 1152, 128, 12870, 39796, 60792, 56400, 33440, 12480, 2688, 256, 48620, 164904, 283208, 304704, 218720, 105600, 33152, 6144
(list; table; graph; listen)
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OFFSET
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2,1
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COMMENT
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If it is required that the paths stay at the same side of the diagonal between intermediate points, then the count of intermediate points becomes an exact count of crossings, and one gets table A039598. Row sum gives A075436.
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EXAMPLE
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{2}, {6, 4}, {20, 24, 8}, {70, 116, 72, 16}, {252, 520, 456, 192, 32}, ...
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MATHEMATICA
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Table[Table[Plus@@Apply[Times, Compositions[n-1-k, k]+1 /. i_Integer->Binomial[2i, i], {1}], {k, 1, n-1}], {n, 2, 12}]
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CROSSREFS
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Cf. A075436, A039598.
Sequence in context: A052100 A079579 A112326 this_sequence A069875 A019088 A096085
Adjacent sequences: A075432 A075433 A075434 this_sequence A075436 A075437 A075438
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 15 2002
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