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Search: id:A151237
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| A151237 |
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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, 0, 0), (0, -1, 0), (0, 1, 0), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 3, 14, 63, 298, 1428, 6906, 33653, 164836, 810060, 3993446, 19727978, 97630392, 483860652, 2400763156, 11923446689, 59266186460, 294785399216, 1467099385086, 7305154655534, 36390338352432, 181345090767820, 903997336345772, 4507679568564746, 22482713911686816, 112160886877865048
(list; graph; listen)
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OFFSET
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0,2
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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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A024037 A100295 A091701 this_sequence A151238 A026243 A058139
Adjacent sequences: A151234 A151235 A151236 this_sequence A151238 A151239 A151240
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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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