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Search: id:A151345
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| A151345 |
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Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 1)} |
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+0
1
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| 1, 1, 6, 55, 644, 8694, 128964, 2045901, 34136960, 592493044, 10614366568, 195164993478, 3667395504304, 70199379387700, 1365217425954360, 26918993235702735, 537238205832405960, 10837199420262489120, 220699085927921277600, 4533022083670853217060, 93823829712145743930720
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MATHEMATICA
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aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, 2 n], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A118836 A079589 A006200 this_sequence A095652 A132689 A140790
Adjacent sequences: A151342 A151343 A151344 this_sequence A151346 A151347 A151348
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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