A151233 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, 1), (0, 1, 0), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 3, 13, 59, 281, 1355, 6613, 32467, 160177, 792707, 3932477, 19541707, 97236105, 484307099, 2414051237, 12040104643, 60078296865, 299892993619, 1497421655949, 7478693480123, 37358671384825, 186648931452395, 932643177692789, 4660703200810867, 23292989642961809, 116420735945141411

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A299502 A151321 A151232 * A151234 A330799 A367057

Adjacent sequences: A151230 A151231 A151232 * A151234 A151235 A151236

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved