A149882 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, 0, 0), (1, 1, -1)}.

1, 2, 5, 14, 43, 147, 523, 1932, 7289, 28034, 110057, 438969, 1774737, 7252025, 29898867, 124323401, 520995759, 2198354226, 9332207929, 39825314924, 170784974678, 735750134895, 3183012540969, 13823368675382, 60242473499159, 263384312542091, 1155038087890992, 5079745113918977

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 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: A137553 A149881 A148334 * A137554 A137555 A137556

Adjacent sequences: A149879 A149880 A149881 * A149883 A149884 A149885

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved