A149640 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), (0, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 69, 273, 1229, 5319, 24415, 109221, 511977, 2334665, 11081693, 51334913, 245326757, 1150864887, 5526605251, 26166379639, 126192482499, 601515563957, 2911677103881, 13952444571557, 67741416520845, 326032539211253, 1586799295785993, 7665223068400129, 37382668907072193, 181139804804208745

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[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: A149637 A149638 A149639 * A353173 A355603 A355507

Adjacent sequences: A149637 A149638 A149639 * A149641 A149642 A149643

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved