A149242 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, 0), (-1, 0, 0), (-1, 1, 1), (0, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 36, 125, 453, 1643, 6160, 23581, 90833, 353457, 1396858, 5547947, 22161694, 89279443, 361655958, 1470244295, 6007452039, 24661753493, 101534196798, 419402648339, 1738678408812, 7226334858703, 30105804655436, 125763533221311, 526549835239967, 2208743593298925, 9284108802310916

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A149239 A149240 A149241 * A149243 A112849 A372721

Adjacent sequences: A149239 A149240 A149241 * A149243 A149244 A149245

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved