A148043 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, 1, 0), (1, 0, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 3, 8, 19, 59, 160, 540, 1623, 5782, 18621, 69373, 235874, 905452, 3204843, 12614718, 46142381, 185206756, 695627226, 2838006420, 10897855854, 45068748877, 176317050793, 737653565662, 2932209752379, 12390079057651, 49934682230051, 212833823146874, 868150513527291, 3728495506882947

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148042 A077269 A294431 * A321255 A243791 A243335

Adjacent sequences: A148040 A148041 A148042 * A148044 A148045 A148046

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved