A151207 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), (0, 1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 0)}

1, 3, 12, 54, 250, 1191, 5755, 28053, 137732, 678922, 3358344, 16650293, 82699123, 411317004, 2047848715, 10204231387, 50878868917, 253815114615, 1266700592913, 6323718535388, 31578149883794, 157722730013935, 787913941758827, 3936644499003767, 19670962071939108, 98303285187905604

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, j, -1 + k, -1 + n] + aux[i, -1 + 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: A151204 A151205 A151206 * A083881 A151208 A055835

Adjacent sequences: A151204 A151205 A151206 * A151208 A151209 A151210

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved