A150741 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 29, 124, 525, 2319, 10398, 47216, 216944, 1005160, 4686453, 21996136, 103666019, 490819904, 2331863129, 11113282758, 53115479147, 254469530539, 1221868994059, 5878557844728, 28332777974260, 136780333469111, 661298741923978, 3201604654757243, 15519682429785727, 75318318097183775

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, 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, 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: A150739 A151301 A150740 * A150742 A150743 A150744

Adjacent sequences: A150738 A150739 A150740 * A150742 A150743 A150744

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved