A148987 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), (0, 1, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 3, 9, 33, 107, 441, 1675, 6829, 26947, 115669, 474921, 2054775, 8602293, 37922487, 162930585, 720453423, 3124409345, 14010065523, 61601080593, 276959416907, 1226301729261, 5558631767127, 24856711661343, 112885565645001, 507054682613963, 2317442672800633, 10478569080891183, 47969825346568941

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, 1 + j, k, -1 + n] + aux[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: A094538 A343735 A037129 * A176812 A192430 A323790

Adjacent sequences: A148984 A148985 A148986 * A148988 A148989 A148990

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved