A149460 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, 0, 0), (-1, 1, 1), (0, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 13, 50, 205, 866, 3749, 16632, 75039, 341961, 1576018, 7327168, 34283739, 161361590, 763453145, 3627427677, 17298560102, 82772495282, 397211322958, 1910994001127, 9215181362223, 44529823106164, 215576405905591, 1045404537941408, 5077352560496235, 24694338511964747, 120257935938127480

Offset

0,3

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, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A364742 A002746 A149459 * A219579 A300122 A149461

Adjacent sequences: A149457 A149458 A149459 * A149461 A149462 A149463

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved