A149712 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, 0), (0, 1, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 17, 71, 285, 1267, 5415, 24929, 109791, 514181, 2325529, 10975213, 50591721, 240309245, 1121609839, 5360709931, 25239934277, 121243984411, 574860107777, 2771889294123, 13219673633385, 63932970161935, 306380916893023, 1485486370030791, 7146790584746631, 34728645396419379, 167628468993741295

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, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149709 A149710 A149711 * A017957 A149713 A149714

Adjacent sequences: A149709 A149710 A149711 * A149713 A149714 A149715

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved