A149058 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, 1), (-1, 0, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 10, 41, 159, 688, 2925, 13046, 58099, 264647, 1209007, 5593147, 25967563, 121512931, 570471691, 2692588141, 12744832317, 60558719347, 288445413396, 1377905039968, 6595712273761, 31644526040701, 152086731460280, 732295734590892, 3531261757118478, 17054388743670055, 82471187201160416

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, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A163843 A149056 A149057 * A151078 A151079 A151080

Adjacent sequences: A149055 A149056 A149057 * A149059 A149060 A149061

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved