A150431 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), (0, 1, 1), (1, 1, 0)}.

1, 2, 7, 24, 98, 381, 1626, 6793, 29484, 128021, 564403, 2500084, 11170691, 50116462, 226143658, 1024155781, 4656130957, 21235409051, 97128731541, 445394455074, 2047219553857, 9429370132204, 43515500709007, 201169480526362, 931494523678825, 4319608455445313, 20058776859173756, 93264842819390272

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[i, -1 + 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: A150429 A150430 A363434 * A302185 A150432 A150433

Adjacent sequences: A150428 A150429 A150430 * A150432 A150433 A150434

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved