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Search: id:A149532
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| A149532 |
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Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 0), (-1, 0, 1), (0, -1, 0), (1, 1, 0)} |
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+0
1
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| 1, 1, 5, 13, 49, 177, 645, 2489, 9621, 37389, 149641, 595069, 2401449, 9767733, 39781097, 163511229, 674229217, 2789228345, 11601713781, 48355166633, 202230993541, 848452552753, 3566524103253, 15033723662041, 63503474794893, 268735010971945, 1139627242648765, 4840572436506129
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A082132 A138277 A084601 this_sequence A149533 A149534 A149535
Adjacent sequences: A149529 A149530 A149531 this_sequence A149533 A149534 A149535
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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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