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A149070
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, 1), (1, -1, 1), (1, 1, -1)}.
0
1, 1, 3, 11, 42, 175, 755, 3318, 14897, 67934, 313320, 1457186, 6834042, 32249951, 152963363, 728772478, 3485974666, 16728898237, 80509755123, 388466875840, 1878628301984, 9102952302638, 44187666497748, 214844863711924, 1046105281413402, 5100271714845970, 24896244561277645, 121660675201413859
OFFSET
0,3
LINKS
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, arXiv:0811.2899 [math.CO].
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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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}]
CROSSREFS
Sequence in context: A151089 A211854 A200212 * A066655 A352684 A302421
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved