A150513 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, 1, -1), (1, 0, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 7, 25, 103, 412, 1767, 7448, 32787, 142374, 636505, 2815581, 12715041, 56978712, 259309861, 1173034613, 5369403379, 24464452536, 112502096435, 515503557713, 2379609901159, 10953729138874, 50723287589467, 234370374685996, 1088228618777343, 5044197283684340, 23475790204876997, 109110088285581615

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, -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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A221453 A097597 A150512 * A150514 A150515 A150516

Adjacent sequences: A150510 A150511 A150512 * A150514 A150515 A150516

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved