A150392 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, 0), (-1, 0, 0), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 7, 24, 90, 357, 1438, 5978, 25263, 108036, 468430, 2047644, 9022100, 40038823, 178625997, 801073426, 3608410329, 16315029606, 74029303462, 336934567335, 1537765898537, 7036309248809, 32269071008867, 148300310592526, 682867977083367, 3149909192000134, 14553709278707920, 67345595327741895

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A052705 A150391 A378585 * A150393 A150394 A151294

Adjacent sequences: A150389 A150390 A150391 * A150393 A150394 A150395

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved