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Search: id:A149455
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| A149455 |
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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, 1, 1)} |
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+0
1
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| 1, 1, 4, 13, 50, 182, 712, 2711, 10672, 41470, 164102, 644580, 2557808, 10108272, 40194806, 159440027, 634857536, 2524253822, 10061284624, 40067909864, 159820748482, 637157976526, 2542888042852, 10145529835268, 40507851460434, 161706752889040, 645859214596938, 2579323889200758
(list; graph; listen)
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OFFSET
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0,3
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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, -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: A149454 A101125 A056275 this_sequence A105968 A149456 A149457
Adjacent sequences: A149452 A149453 A149454 this_sequence A149456 A149457 A149458
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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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