A151077 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), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 3, 10, 40, 172, 761, 3484, 16219, 76413, 364192, 1748227, 8443769, 40994937, 199796255, 977047346, 4791306327, 23549578328, 115979651288, 572148949214, 2826591966146, 13981867047153, 69237078504933, 343183608015103, 1702466147416325, 8451820517056851, 41986153381168419, 208695902977464969

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A151074 A151075 A151076 * A300043 A258973 A217885

Adjacent sequences: A151074 A151075 A151076 * A151078 A151079 A151080

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved