A151073 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, 0), (0, 1, 1), (1, 0, 0)}

1, 3, 10, 39, 163, 698, 3093, 13980, 63817, 295250, 1378577, 6473083, 30601533, 145413606, 693468104, 3320340108, 15949166440, 76800820187, 370781922113, 1793994166695, 8695586394877, 42223940576424, 205352852892638, 1000056842156015, 4876643618508198, 23808301200207172, 116355162538349843

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A367258 A338185 A151072 * A363555 A063688 A245378

Adjacent sequences: A151070 A151071 A151072 * A151074 A151075 A151076

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved