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Search: id:A150967
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| A150967 |
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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), (0, 1, -1), (1, 0, 1), (1, 1, 1)} |
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+0
1
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| 1, 2, 9, 36, 153, 702, 3185, 14650, 69150, 325689, 1541121, 7388523, 35382543, 169913378, 821846528, 3973759409, 19247428324, 93639904181, 455548738095, 2218883275006, 10839127251592, 52954373841996, 258939021795761, 1268715094550086, 6217377584328286, 30489452492906125, 149733437038438819
(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[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: A037730 A029874 A052834 this_sequence A121769 A006782 A150968
Adjacent sequences: A150964 A150965 A150966 this_sequence A150968 A150969 A150970
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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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