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A149494
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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, 1), (-1, 1, 1), (1, -1, 1), (1, 0, -1), (1, 1, 0)}
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0
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1, 1, 4, 14, 63, 255, 1208, 5300, 25641, 117338, 573977, 2692760, 13258820, 63201086, 312496952, 1505774619, 7466107255, 36252353187, 180100006382, 879419719458, 4375006206173, 21453621299034, 106838674543666, 525615953548604, 2619579742968437, 12920694277538078, 64432646543341008, 318456275901964557
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..27.
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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A009339 A050912 A250399 * A322206 A149495 A137956
Adjacent sequences: A149491 A149492 A149493 * A149495 A149496 A149497
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers, Nov 18 2008
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STATUS
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approved
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