A150028 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, -1), (-1, 0, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 6, 16, 54, 169, 602, 1988, 7290, 25170, 93811, 330902, 1249367, 4499607, 17116040, 62347523, 238894837, 880763604, 3388972673, 12582449763, 48639631649, 182013638337, 705478480829, 2652531544952, 10314218236630, 38995799156417, 151909821456349, 576310438021719, 2250333836996630

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A218779 A241066 A045696 * A147730 A147729 A147728

Adjacent sequences: A150025 A150026 A150027 * A150029 A150030 A150031

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved