A148905 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, 1, -1), (0, 1, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 3, 8, 32, 105, 425, 1555, 6559, 25671, 110019, 449431, 1958255, 8227895, 36275689, 155511325, 692565424, 3013775389, 13531258452, 59576885327, 269293212642, 1196878011947, 5440316586159, 24367302407841, 111282324988116, 501671079606549, 2300289896988672, 10427016510207755, 47976617932506297

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[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, 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: A148903 A148904 A218882 * A148906 A148907 A148908

Adjacent sequences: A148902 A148903 A148904 * A148906 A148907 A148908

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved