A148279 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, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 16, 46, 167, 495, 2102, 7198, 29506, 101661, 447830, 1662061, 7152135, 26571095, 119610098, 465593444, 2056854630, 7994549636, 36480375305, 146548393847, 658189128755, 2636694594312, 12142942495573, 49881495189460, 226580814242014, 927564903712122, 4300144504106823

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, 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, -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: A133465 A110128 A370658 * A101061 A148280 A112638

Adjacent sequences: A148276 A148277 A148278 * A148280 A148281 A148282

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved