A151187 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), (0, 0, 1), (0, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 3, 12, 51, 229, 1057, 4973, 23707, 114084, 552863, 2693562, 13177746, 64682128, 318329991, 1570030555, 7757317348, 38384755215, 190172212694, 943178242919, 4682003520932, 23259791365273, 115629962700026, 575158307708094, 2862364197846018, 14251344892802178, 70983481869982844, 353679253984093680

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A377582 A151185 A151186 * A340893 A151188 A151189

Adjacent sequences: A151184 A151185 A151186 * A151188 A151189 A151190

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved