A150350 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), (-1, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 23, 91, 338, 1431, 5648, 24811, 101648, 455335, 1912221, 8669523, 37049004, 169499233, 733925969, 3382008835, 14796764162, 68569120311, 302530897701, 1408150982229, 6255959105012, 29224541288539, 130590664138560, 611924555411041, 2747986960072224, 12910255335278135, 58225602748741277

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + 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: A150347 A150348 A150349 * A150351 A150352 A150353

Adjacent sequences: A150347 A150348 A150349 * A150351 A150352 A150353

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved