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A148651 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, 0), (-1, 1, -1), (0, 1, -1), (1, 0, 1)}. 0
1, 1, 3, 6, 24, 64, 225, 744, 2702, 9380, 34049, 127464, 472776, 1769652, 6775136, 26075746, 100305210, 389461385, 1532644757, 6016110125, 23710831146, 94354307856, 376564777974, 1502996930197, 6032442936774, 24345393485794, 98250061661231, 397450217055413, 1615949284188521, 6581022529179247 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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}]
CROSSREFS
Sequence in context: A271428 A148649 A148650 * A148652 A148653 A148654
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified July 22 20:14 EDT 2024. Contains 374540 sequences. (Running on oeis4.)