A150540 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, 0, 0), (0, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 103, 427, 1831, 8019, 35703, 161260, 736399, 3391747, 15739863, 73517590, 345214013, 1628487358, 7713911678, 36670988713, 174874568893, 836288878658, 4009503724542, 19266659826618, 92770506872980, 447535198947326, 2162638003998060, 10466783750848901, 50729802575587416, 246198769403087542

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, j, -1 + k, -1 + n] + aux[1 + i, 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: A264224 A150538 A150539 * A150541 A150542 A150543

Adjacent sequences: A150537 A150538 A150539 * A150541 A150542 A150543

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved