A150225 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), (0, 1, -1), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 21, 84, 348, 1497, 6588, 29406, 133422, 611349, 2827460, 13181010, 61823155, 291598421, 1381827519, 6574502260, 31392797767, 150364898176, 722203336247, 3477336530586, 16779860469626, 81132027352466, 392985700120555, 1906635280947413, 9264115396022671, 45074412891336464, 219582154950721075

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A150222 A150223 A150224 * A123922 A350798 A326276

Adjacent sequences: A150222 A150223 A150224 * A150226 A150227 A150228

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved