A148479 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, 0, 1), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 6, 20, 69, 249, 943, 3694, 14787, 60275, 249800, 1049734, 4461021, 19139414, 82811849, 360977604, 1583710287, 6987944009, 30991468703, 138079317470, 617743638777, 2774018014177, 12499289481540, 56494789617004, 256073683368157, 1163736962136064, 5301389067713143, 24204207325920089

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A047036 A199248 A148478 * A150124 A045631 A275046

Adjacent sequences: A148476 A148477 A148478 * A148480 A148481 A148482

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved