A149560 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), (-1, 1, -1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 13, 59, 193, 901, 3271, 15491, 59357, 283649, 1126583, 5423549, 22084073, 106895167, 443477691, 2155148575, 9072490125, 44228408951, 188384093539, 920685526563, 3959627932739, 19391369317233, 84077089660291, 412450227537063, 1800727501511157, 8846406937814897, 38854506687500175

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, 1 + j, k, -1 + n] + aux[1 + 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: A149557 A149558 A149559 * A149561 A149562 A149563

Adjacent sequences: A149557 A149558 A149559 * A149561 A149562 A149563

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved