A149442 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 47, 181, 740, 3069, 13058, 56579, 249045, 1108338, 4984405, 22604514, 103286755, 474904820, 2195871006, 10202830924, 47613446894, 223056800199, 1048606940183, 4945029338582, 23386110970430, 110883597202716, 526987226077011, 2509980861139166, 11978514690153192, 57270458107910969

Offset

0,3

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A163862 A149440 A149441 * A078468 A354339 A149443

Adjacent sequences: A149439 A149440 A149441 * A149443 A149444 A149445

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved