A150658 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, 1), (1, 1, 0)}.

1, 2, 7, 28, 120, 536, 2457, 11481, 54360, 259969, 1252706, 6072223, 29572252, 144564197, 708884636, 3484931078, 17168524909, 84731554148, 418805940619, 2072716595002, 10269460176509, 50929639896861, 252786813629413, 1255605670244016, 6240630233618970, 31034662772521170, 154411925525049741

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, -1 + 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: A005436 A150656 A150657 * A026770 A241371 A368970

Adjacent sequences: A150655 A150656 A150657 * A150659 A150660 A150661

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved