A150260 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, 1, 1), (0, 0, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 22, 87, 351, 1453, 6164, 26598, 116082, 511162, 2268857, 10139092, 45562967, 205713249, 932569833, 4242893713, 19365253835, 88635249152, 406706356349, 1870413057392, 8619546163502, 39796241572490, 184051950457152, 852546973495396, 3954779801488103, 18369845872214594, 85433118781300358

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150259 A165531 A374542 * A165532 A165533 A164651

Adjacent sequences: A150257 A150258 A150259 * A150261 A150262 A150263

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved