A150243 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, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 22, 83, 339, 1410, 6012, 26174, 115142, 514238, 2314469, 10510960, 48065473, 221035780, 1022285164, 4747939570, 22147857201, 103678307003, 486943792720, 2293897314876, 10834524859103, 51302647093049, 243458624316611, 1157769043129910, 5516221587170438, 26328660427737035, 125872526752387976

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[-1 + i, j, k, -1 + n] + aux[i, -1 + 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: A150240 A150241 A150242 * A200316 A164870 A121686

Adjacent sequences: A150240 A150241 A150242 * A150244 A150245 A150246

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved