A149224 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, 1, 0), (0, 1, -1), (1, -1, 1), (1, 1, 0)}

1, 1, 4, 10, 44, 150, 661, 2591, 11541, 48443, 219710, 956105, 4411606, 19644676, 91797778, 415976400, 1960755775, 9009548272, 42741998435, 198551589284, 946944361740, 4436661562547, 21254662316078, 100271797248771, 482176895814109, 2287810098061031, 11035948199774608, 52617111040702537

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149222 A264571 A149223 * A149225 A122648 A058819

Adjacent sequences: A149221 A149222 A149223 * A149225 A149226 A149227

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved