A150502 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), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 25, 102, 403, 1737, 7244, 31911, 137926, 615976, 2717221, 12268696, 54843343, 249585694, 1127105125, 5158721778, 23478404133, 107958051841, 494269144847, 2281524240969, 10495551496764, 48601873781132, 224465125580471, 1042241504635216, 4829414998947986, 22476564935460318, 104439565069138006

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A150500 A221455 A150501 * A150503 A150504 A150505

Adjacent sequences: A150499 A150500 A150501 * A150503 A150504 A150505

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved