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A149472 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), (0, -1, 1), (0, 1, 1), (1, -1, 0), (1, 1, -1)}. 0
1, 1, 4, 13, 55, 218, 938, 4066, 18186, 82109, 376555, 1739578, 8112029, 38060074, 179648530, 851992988, 4058089997, 19398498945, 93031571639, 447417004233, 2157208439028, 10424242302643, 50474493209864, 244841799877749, 1189629245296910, 5788729912510802, 28206143441989132, 137607455387105965 (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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + 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}]
CROSSREFS
Sequence in context: A229182 A149470 A149471 * A149473 A365854 A188205
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified June 19 09:28 EDT 2024. Contains 373499 sequences. (Running on oeis4.)