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Search: id:A150664
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| A150664 |
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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, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)} |
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+0
1
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| 1, 2, 7, 29, 129, 598, 2835, 13644, 66319, 324630, 1597025, 7885507, 39041941, 193699338, 962518555, 4788722705, 23847568557, 118848810902, 592658978457, 2956802946625, 14757301904357, 73676132704272, 367922865754725, 1837709064234518, 9180591215488059, 45869654339178428, 229208480098828445
(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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A126568 A150663 A054321 this_sequence A132262 A007852 A110576
Adjacent sequences: A150661 A150662 A150663 this_sequence A150665 A150666 A150667
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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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