A148902 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, 1), (-1, 1, 1), (0, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 8, 31, 114, 475, 1987, 8682, 38428, 173636, 792939, 3663783, 17065149, 80076371, 377979137, 1793374394, 8545969754, 40879106065, 196184628494, 944237293800, 4556163983762, 22034067907113, 106772807172070, 518329967949744, 2520304811567726, 12272504998264021, 59839464232713031

Offset

0,3

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148899 A148900 A148901 * A213092 A352624 A108492

Adjacent sequences: A148899 A148900 A148901 * A148903 A148904 A148905

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved