A150981 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, 1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 36, 173, 769, 3762, 17511, 86361, 411423, 2037985, 9839317, 48868281, 237931344, 1183748118, 5796419938, 28871992103, 141951105936, 707648354549, 3489653338760, 17407086186809, 86036783957843, 429365366810146, 2125989783087252, 10613449124746823, 52627074692715082, 262798854860711897

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A150979 A150980 A137955 * A150982 A003161 A305206

Adjacent sequences: A150978 A150979 A150980 * A150982 A150983 A150984

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved