A148058 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, 1), (-1, 1, 0), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 3, 10, 22, 67, 154, 568, 1550, 5395, 14789, 57575, 175048, 652147, 1970803, 7935097, 25771324, 100086938, 321963277, 1326586894, 4506499578, 18002375075, 60497955037, 253509127261, 889894534837, 3628463886414, 12595624469633, 53465517732990, 192448886725638, 797022172851503, 2837071346803048

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 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] + 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: A285794 A148056 A148057 * A148059 A089880 A271740

Adjacent sequences: A148055 A148056 A148057 * A148059 A148060 A148061

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved