A150529 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, -1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 25, 106, 437, 1929, 8488, 38396, 174507, 803900, 3722663, 17371905, 81437630, 383684351, 1814422663, 8611181387, 40990036508, 195652384453, 936119745972, 4488768349921, 21566203619958, 103800173160993, 500414792081605, 2416084626457006, 11681304992422310, 56548686955077475, 274071984546734932

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A150526 A150527 A150528 * A286761 A150530 A150531

Adjacent sequences: A150526 A150527 A150528 * A150530 A150531 A150532

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved