A149369 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, 0, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 12, 45, 171, 687, 2803, 11748, 49831, 214434, 931716, 4085156, 18040522, 80183435, 358314337, 1608920279, 7254733913, 32835218026, 149109378700, 679164584418, 3101883535311, 14201896280766, 65169414956550, 299665789841870, 1380552538613722, 6371296684194483, 29451369951867444

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[i, 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: A149367 A149368 A200539 * A151432 A188312 A006735

Adjacent sequences: A149366 A149367 A149368 * A149370 A149371 A149372

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved