A148954 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, 0), (-1, 1, 1), (0, -1, 0), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 9, 30, 103, 384, 1448, 5657, 22484, 91109, 373965, 1556099, 6536793, 27720857, 118517912, 510272098, 2210542606, 9632036562, 42184306699, 185588435364, 819950687056, 3636717337195, 16186362286732, 72275528903043, 323701780511341, 1453804685181711, 6546093937183779, 29546360820193525

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A007453 A148952 A148953 * A289602 A148955 A119372

Adjacent sequences: A148951 A148952 A148953 * A148955 A148956 A148957

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved