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Search: id:A151220
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| A151220 |
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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), (0, 0, 1), (0, 1, -1), (1, 0, 1), (1, 1, 1)} |
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+0
1
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| 1, 3, 13, 56, 258, 1208, 5749, 27646, 133968, 652592, 3193440, 15676731, 77165036, 380650135, 1880986314, 9308619584, 46122972729, 228769029625, 1135698530874, 5642322475774, 28050311064755, 139529410550457, 694400800401623, 3457363880665795, 17220587369234781, 85802417773381773
(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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A010903 A010920 A095934 this_sequence A151221 A020515 A049086
Adjacent sequences: A151217 A151218 A151219 this_sequence A151221 A151222 A151223
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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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