A149053 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, 1), (1, 1, -1)}.

1, 1, 3, 10, 40, 154, 677, 2815, 12795, 55992, 260063, 1171488, 5519680, 25390443, 120790770, 563597058, 2701493583, 12740989900, 61404619312, 291993134549, 1413481335777, 6764629214481, 32860034334098, 158081263555453, 770095715645065, 3720320797966003, 18166699427992532, 88071146741870330

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, -1 + 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: A318118 A149052 A009692 * A149054 A149055 A254535

Adjacent sequences: A149050 A149051 A149052 * A149054 A149055 A149056

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved