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A148768
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, 0), (-1, 0, 0), (0, 1, -1), (1, 0, 1)}.
0
1, 1, 3, 8, 20, 67, 205, 624, 2153, 7063, 23186, 81508, 278425, 948750, 3384908, 11847193, 41298456, 149008573, 529767107, 1876095094, 6825387722, 24534558825, 87900272775, 321769750934, 1166215560501, 4215150277315, 15504036331765, 56555181632041, 205814795959039, 759930513178342, 2786331126194799
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, j, k, -1 + n] + aux[1 + i, 1 + 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: A354519 A302674 A108189 * A110861 A027320 A027319
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved