A151019 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, 0), (-1, -1, 1), (-1, 0, 0), (1, 1, 0), (1, 1, 1)}.

1, 2, 10, 32, 160, 584, 2920, 11360, 56800, 229568, 1147840, 4759424, 23797120, 100509824, 502549120, 2152467968, 10762339840, 46606146560, 233030732800, 1018160390144, 5090801950720, 22407240077312, 112036200386560, 496198838730752, 2480994193653760, 11046580426440704, 55232902132203520

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A032095 A328039 A264960 * A329427 A004028 A263839

Adjacent sequences: A151016 A151017 A151018 * A151020 A151021 A151022

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved