A150665 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, 0), (-1, 0, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 8, 24, 102, 353, 1577, 5886, 26998, 105443, 491899, 1981368, 9351104, 38515589, 183306859, 767905242, 3677958607, 15614342446, 75157817745, 322531713688, 1558640776522, 6748618941080, 32718826459406, 142732980763735, 693872617090262, 3046416114068730, 14843444538063504, 65531667579436177

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, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A362139 A060899 A213951 * A150666 A150667 A150668

Adjacent sequences: A150662 A150663 A150664 * A150666 A150667 A150668

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved