A150376 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, 1), (1, 1, 0)}.

1, 2, 7, 23, 96, 354, 1558, 6126, 27515, 112507, 512529, 2147588, 9885539, 42148934, 195391127, 844315803, 3934322576, 17179647304, 80384018006, 353955909902, 1661689382158, 7367702237571, 34682335239711, 154675340648931, 729757290756506, 3270774292939276, 15461202200359990, 69595681801664499

Offset

0,2

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, j, -1 + 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: A150374 A326648 A150375 * A150377 A150378 A150379

Adjacent sequences: A150373 A150374 A150375 * A150377 A150378 A150379

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved