A148965 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, -1)}

1, 1, 3, 9, 31, 105, 411, 1549, 6231, 25289, 104763, 440389, 1878783, 8081057, 35193059, 154280861, 682012423, 3034589177, 13581750123, 61124230837, 276429656655, 1255645709073, 5727450413555, 26220958181069, 120462701394071, 555185781221289, 2566283254104699, 11895177945168997, 55277310558686175

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, 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: A221440 A289599 A148964 * A130620 A202246 A225340

Adjacent sequences: A148962 A148963 A148964 * A148966 A148967 A148968

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved