A149482 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, 0, 1), (-1, 1, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 13, 58, 226, 1055, 4519, 21614, 97094, 471010, 2178613, 10660517, 50257832, 247314696, 1181334243, 5835644820, 28137910424, 139376200116, 676714986878, 3358628183403, 16393168567510, 81481596697479, 399325900478770, 1987060483010033, 9769457634905532, 48655357050063238, 239829359080746283

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, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A283612 A039626 A149481 * A149483 A149484 A149485

Adjacent sequences: A149479 A149480 A149481 * A149483 A149484 A149485

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved