A148400 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), (-1, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 16, 54, 197, 746, 2876, 11390, 45977, 188066, 780848, 3280312, 13909971, 59533135, 256759223, 1114687983, 4869337791, 21385124366, 94368601473, 418274225010, 1861248654027, 8311998648668, 37242997500962, 167375917694208, 754308894036624, 3408201201827853, 15436011804303550

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A149965 A149966 A149967 * A052836 A108526 A363201

Adjacent sequences: A148397 A148398 A148399 * A148401 A148402 A148403

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved