A149900 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, 0), (1, 0, 1)}.

1, 2, 5, 14, 47, 159, 570, 2073, 7937, 30410, 119925, 474811, 1924495, 7807044, 32203887, 133069917, 557221720, 2335779862, 9894442363, 41963425550, 179491780393, 768567676097, 3314106748325, 14305762765069, 62114424112373, 269972686309324, 1179211837551930, 5155802812760365

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 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: A006216 A148337 A149899 * A149901 A149902 A047026

Adjacent sequences: A149897 A149898 A149899 * A149901 A149902 A149903

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved