A150396 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, 0, 1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 7, 24, 92, 361, 1475, 6134, 26003, 111652, 484831, 2123974, 9376383, 41655965, 186092797, 835332330, 3765485210, 17037280894, 77343518126, 352162305344, 1607799039422, 7358381131226, 33752125518375, 155133966606545, 714378468745611, 3295358655374578, 15225594623554362, 70452034520063898

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, 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] + 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: A196470 A339785 A150395 * A150397 A150398 A150399

Adjacent sequences: A150393 A150394 A150395 * A150397 A150398 A150399

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved