A149429 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, 0, 0), (0, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 4, 13, 44, 156, 560, 2065, 7702, 28898, 109382, 415768, 1589470, 6102378, 23500260, 90781393, 351496758, 1364024040, 5303511032, 20655297846, 80569251748, 314690828550, 1230632550218, 4817793313450, 18879891033224, 74053400563496, 290704112428572, 1142059574537634, 4489837317690300

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A229397 A283110 A149428 * A045652 A149430 A124463

Adjacent sequences: A149426 A149427 A149428 * A149430 A149431 A149432

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved