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A149830
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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), (-1, 1, -1), (0, 0, 1), (1, -1, 0), (1, 0, 0)}
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0
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1, 2, 4, 10, 28, 85, 282, 961, 3348, 12090, 44786, 168404, 643901, 2505895, 9858281, 39170311, 157508249, 638763140, 2608585552, 10740130403, 44524221312, 185571516895, 777920112939, 3279160755069, 13883250806461, 59032846349700, 252125642478286, 1080805369925001, 4648940165418700
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..28.
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, j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A149827 A149828 A149829 * A027412 A030277 A149831
Adjacent sequences: A149827 A149828 A149829 * A149831 A149832 A149833
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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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