A149817 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), (0, 0, 1), (0, 1, 0), (1, -1, -1)}.

1, 2, 4, 10, 26, 76, 248, 810, 2710, 9279, 32769, 118679, 434731, 1605567, 6001035, 22816644, 87542063, 337991886, 1312648077, 5140546851, 20310742444, 80662660780, 321579922685, 1287839804194, 5189476064752, 21015223863898, 85377876326755, 347860007510905, 1422691033654448, 5843668040434633

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A148100 A149815 A149816 * A149818 A148101 A052854

Adjacent sequences: A149814 A149815 A149816 * A149818 A149819 A149820

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved