A150920 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, 1, -1), (1, -1, 1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 32, 155, 644, 3175, 14098, 69976, 321879, 1602721, 7531433, 37563469, 179013811, 893681771, 4300873876, 21483003773, 104127014063, 520295910233, 2535398215467, 12671477292433, 62004023022238, 309928733352159, 1521498848117653, 7605955483533491, 37437013573708917, 187158809268065886

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150917 A150918 A150919 * A013501 A179230 A114853

Adjacent sequences: A150917 A150918 A150919 * A150921 A150922 A150923

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved