A150617 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), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 27, 113, 483, 2138, 9681, 44374, 205500, 961614, 4532177, 21472917, 102258257, 489141279, 2347573314, 11300344747, 54548339666, 263926643851, 1279497594561, 6214413418672, 30233348558479, 147297034473933, 718569377619361, 3509725616656089, 17161306005034007, 83994842745043322

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[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: A192455 A150615 A150616 * A150618 A150619 A150620

Adjacent sequences: A150614 A150615 A150616 * A150618 A150619 A150620

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved