A150364 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, 0), (1, 1, 0)}.

1, 2, 7, 23, 92, 360, 1515, 6410, 27833, 122316, 543974, 2443399, 11063866, 50447923, 231486525, 1067574203, 4947914367, 23023490010, 107546786397, 504019149052, 2369384026520, 11168991236308, 52783105573185, 250022457719306, 1186837485357488, 5644935205136720, 26897964605753765, 128386130710878982

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[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: A150361 A150362 A150363 * A093636 A150365 A150366

Adjacent sequences: A150361 A150362 A150363 * A150365 A150366 A150367

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved