A150591 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, 0, 0), (0, 0, -1), (0, 1, 0), (1, 1, 1)}.

1, 2, 7, 27, 105, 426, 1787, 7590, 32633, 142152, 624659, 2763357, 12305393, 55103828, 247872791, 1119588403, 5075796897, 23086174696, 105306348827, 481622980387, 2207998493273, 10144524748848, 46701478420759, 215390610021262, 995075944131209, 4604311511035654, 21335578867637575, 98999148480162529

Offset

0,2

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A329011 A037381 A129013 * A150592 A150593 A024429

Adjacent sequences: A150588 A150589 A150590 * A150592 A150593 A150594

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved