A150894 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, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 34, 155, 720, 3415, 16383, 79328, 386470, 1891850, 9294566, 45795647, 226153248, 1118854674, 5543559786, 27500181154, 136560136318, 678706790731, 3375612040066, 16799183694507, 83647085652955, 416685864883258, 2076517827764731, 10351646065062625, 51619218086553474, 257469584368181012

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + 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: A150892 A150893 A235038 * A150895 A150896 A150897

Adjacent sequences: A150891 A150892 A150893 * A150895 A150896 A150897

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved