A150628 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, 1), (0, 1, 0), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 2, 7, 27, 114, 504, 2294, 10656, 50218, 239227, 1149063, 5554590, 26988272, 131667326, 644515544, 3163659940, 15564904380, 76726441320, 378841644950, 1873181975221, 9273129911486, 45954263710921, 227939234305642, 1131504698218510, 5620765232504488, 27938330085282670, 138944267750797255

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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

Sequence in context: A150625 A150626 A150627 * A106225 A127897 A180473

Adjacent sequences: A150625 A150626 A150627 * A150629 A150630 A150631

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved