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A149758
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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, 0), (-1, 0, 1), (0, -1, 0), (0, 0, -1), (1, 1, 1)}
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0
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1, 1, 5, 19, 69, 277, 1185, 5009, 21325, 92733, 408629, 1807995, 8038887, 35981881, 162014757, 732494001, 3321753179, 15111904573, 68984336243, 315806352009, 1448850054545, 6660481232055, 30684420675499, 141639855244171, 654874542763787, 3032247286729153, 14060715339443201, 65292539049162537
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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
| Sequence in context: A047145 A055991 A030662 * A026590 A095073 A128349
Adjacent sequences: A149755 A149756 A149757 * A149759 A149760 A149761
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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