A149698 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, 0, 0), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 69, 267, 1167, 4855, 21419, 92169, 413653, 1820575, 8237365, 36789927, 167756317, 757342581, 3471510325, 15797575547, 72748645289, 333122881165, 1539530130895, 7084568397845, 32844125083437, 151753994554771, 705352964589465, 3269966289899371, 15233634774302207, 70822405260256391

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A096980 A339684 A149697 * A149699 A151276 A272743

Adjacent sequences: A149695 A149696 A149697 * A149699 A149700 A149701

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved