A150539 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, 0), (0, 0, 1), (0, 1, -1), (1, 1, 0)}.

1, 2, 7, 26, 103, 426, 1817, 7905, 34999, 156978, 711572, 3254200, 14992984, 69508490, 324005487, 1517421717, 7135832181, 33679784580, 159477986279, 757336398740, 3605893799280, 17209257753242, 82307977414514, 394432975779016, 1893578180925439, 9105600973099922, 43852562469867462, 211491091134032890

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, 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: A119243 A264224 A150538 * A150540 A150541 A150542

Adjacent sequences: A150536 A150537 A150538 * A150540 A150541 A150542

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved