

A150168


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, 1), (0, 1, 0), (1, 0, 1), (1, 1, 0)}.


0



1, 2, 6, 20, 75, 297, 1223, 5178, 22441, 98884, 442283, 2000916, 9142251, 42116199, 195395624, 912044028, 4279777216, 20176137436, 95507078481, 453744740526, 2162709310394, 10338309423180, 49549707152860, 238047836414608, 1146105257197884, 5528901726159039, 26719869652877299, 129343971140839144
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OFFSET

0,2


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, k, 1 + n] + aux[1 + i, j, 1 + k, 1 + n] + aux[i, 1 + j, k, 1 + n] + aux[1 + i, 1 + j, 1 + 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



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



