A150094 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, 1, 0), (0, 0, 1), (1, 0, -1), (1, 0, 0)}.

1, 2, 6, 19, 66, 247, 966, 3907, 16161, 68187, 292988, 1277679, 5638228, 25121213, 112897471, 511377308, 2332359467, 10700837502, 49349356380, 228656721764, 1064040168553, 4970759755902, 23302285912883, 109582451702144, 516824544225503, 2444056861503320, 11586473757680157, 55052037361026731

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A190737 A150092 A150093 * A305118 A234010 A360212

Adjacent sequences: A150091 A150092 A150093 * A150095 A150096 A150097

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved