A150656 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, 0, 0), (0, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 28, 120, 533, 2431, 11306, 53313, 253981, 1219497, 5892033, 28610302, 139489397, 682344795, 3347079833, 16456433524, 81069630699, 400043687892, 1976878885936, 9781172827062, 48447253861374, 240190177910842, 1191787510194140, 5917756953017000, 29403129583489506, 146176214940053868

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150654 A150655 A005436 * A150657 A150658 A026770

Adjacent sequences: A150653 A150654 A150655 * A150657 A150658 A150659

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved