A149314 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, 1), (-1, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 50, 167, 771, 2807, 13280, 51002, 243916, 970970, 4674782, 19064034, 92340774, 383539818, 1864849365, 7858691140, 38326717947, 163387754402, 798855263483, 3438187209017, 16843186616739, 73075209629276, 358580295925148, 1566394001078123, 7697124456690464, 33822992737733424

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, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A296532 A149312 A149313 * A149315 A149316 A271426

Adjacent sequences: A149311 A149312 A149313 * A149315 A149316 A149317

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved