A150278 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, 1), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 23, 89, 356, 1488, 6314, 27245, 118980, 524095, 2329881, 10420569, 46855042, 211754434, 960734442, 4374585435, 19982883368, 91529713105, 420306854683, 1934383456041, 8920543113198, 41214253945576, 190735176033572, 884063398111250, 4103502859495205, 19071907781880600, 88748781388751468

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A228392 A190910 A150277 * A150279 A150280 A303071

Adjacent sequences: A150275 A150276 A150277 * A150279 A150280 A150281

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved