A151210 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, 0, 1), (1, 0, 0), (1, 1, 0), (1, 1, 1)}

1, 3, 13, 53, 249, 1114, 5374, 25006, 122170, 580646, 2856900, 13755459, 67974232, 330102232, 1635929596, 7992375813, 39687844586, 194746571299, 968445955527, 4767806401540, 23734898099668, 117148056572172, 583654571798332, 2886514612797420, 14390217584566146, 71282430731218510, 355542014797764623

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

Sequence in context: A065838 A052990 A151209 * A151211 A367755 A121240

Adjacent sequences: A151207 A151208 A151209 * A151211 A151212 A151213

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved