A148575 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, 0, 0), (-1, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 6, 20, 50, 181, 513, 1981, 6087, 24450, 79265, 326192, 1098561, 4604660, 15968636, 67934917, 241144724, 1037831560, 3753744245, 16303956286, 59889623003, 262114436704, 975484574708, 4296973313554, 16171297126704, 71624751796375, 272169868078628, 1211149718585558, 4641314003656235

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A148574 A005558 A138350 * A148576 A148577 A148578

Adjacent sequences: A148572 A148573 A148574 * A148576 A148577 A148578

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved