A150308 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, -1, 0), (-1, 0, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 84, 293, 1240, 4656, 20363, 80023, 357202, 1447365, 6552397, 27145352, 124153417, 523071534, 2410975045, 10293066163, 47732356116, 205975042397, 959841636269, 4178736283241, 19550805153692, 85752038453092, 402540692582469, 1776854677123549, 8364483169632075, 37125294976403035

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, -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, 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: A150306 A150307 A321283 * A150309 A150310 A150311

Adjacent sequences: A150305 A150306 A150307 * A150309 A150310 A150311

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved