A148770 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, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 8, 22, 69, 221, 708, 2361, 7974, 27222, 93714, 326352, 1145719, 4034121, 14309172, 51037561, 182498166, 655374727, 2362467329, 8537671487, 30934793788, 112387091102, 409219645036, 1492785764154, 5456154314546, 19978612353018, 73263269523341, 269061539555529, 989559354926761, 3643958970157747

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A260661 A171841 A233449 * A369791 A189944 A148771

Adjacent sequences: A148767 A148768 A148769 * A148771 A148772 A148773

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved