A149393 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), (-1, 1, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 50, 182, 807, 3258, 14877, 63387, 294952, 1300716, 6129517, 27674324, 131595940, 604281169, 2892883029, 13453559074, 64742577763, 304056392684, 1469273261363, 6954085250877, 33716862066897, 160587550839824, 780775684758989, 3737950408475090, 18216415274109001, 87587232521724541

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149390 A149391 A149392 * A104708 A149394 A149395

Adjacent sequences: A149390 A149391 A149392 * A149394 A149395 A149396

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved