A150558 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, 0), (0, 1, 1), (1, -1, 0), (1, 1, 0)}.

1, 2, 7, 26, 106, 438, 1886, 8208, 36645, 164838, 749978, 3436717, 15865958, 73717234, 344237449, 1614232355, 7599086216, 35897479082, 170135432788, 808558437606, 3851956705719, 18391549249968, 87996068206656, 421846643489797, 2025805986376666, 9743584249035559, 46932362767850800, 226373652767896536

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A052706 A150556 A150557 * A150559 A150560 A150561

Adjacent sequences: A150555 A150556 A150557 * A150559 A150560 A150561

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved