A148418 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, 1, 1), (1, 0, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 18, 55, 205, 682, 2716, 9813, 40365, 152018, 638659, 2490436, 10647216, 42586598, 184288275, 751806906, 3286398696, 13626370299, 60049705914, 252280262853, 1119262471369, 4754854761894, 21216470260315, 90986300896046, 407975808852343, 1763876164303166, 7942893485431455

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A293964 A275079 A148417 * A148419 A148420 A148421

Adjacent sequences: A148415 A148416 A148417 * A148419 A148420 A148421

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved