A148644 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), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 6, 23, 61, 253, 756, 3261, 10535, 46682, 159070, 717567, 2541790, 11617044, 42393793, 195701362, 731199645, 3401970662, 12956824923, 60665684810, 234762379562, 1104940403944, 4333806993682, 20487068668591, 81287047949830, 385698194882121, 1545739799968649, 7357901668028804

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A151443 A148643 A240646 * A148645 A148646 A148647

Adjacent sequences: A148641 A148642 A148643 * A148645 A148646 A148647

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved