A149312 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), (-1, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 50, 164, 758, 2751, 13170, 50788, 244390, 974152, 4753878, 19509060, 95424222, 398465821, 1962358882, 8331842126, 41081869566, 176337842820, 872788848934, 3786709380634, 18755451523772, 81985079770186, 407015868052254, 1792518475634964, 8902849548401976, 39424036762710462

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + 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, 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: A212086 A361359 A296532 * A149313 A149314 A149315

Adjacent sequences: A149309 A149310 A149311 * A149313 A149314 A149315

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved