A150621 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), (0, 0, 1), (0, 1, -1), (1, -1, 0), (1, 1, 0)}.

1, 2, 7, 27, 113, 491, 2201, 10076, 46852, 220491, 1047338, 5012115, 24131162, 116756686, 567248282, 2765433191, 13521407189, 66277140987, 325563517576, 1602182917170, 7897467757215, 38982953013195, 192662950420401, 953223540663176, 4720739548472014, 23398999569950504, 116068945511066928

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A150618 A150619 A150620 * A150622 A150623 A150624

Adjacent sequences: A150618 A150619 A150620 * A150622 A150623 A150624

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved