A151238 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), (1, -1, 0), (1, 0, 0), (1, 1, 0), (1, 1, 1)}.

1, 3, 14, 63, 302, 1440, 7020, 34175, 167978, 825688, 4078284, 20152606, 99849580, 494979560, 2457666200, 12208697151, 60709727410, 302015454120, 1503479139724, 7487167558122, 37303246441268, 185909155131480, 926845403327304, 4621854727637926, 23053660002910820, 115013127548121776

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, 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: A091701 A242637 A151237 * A026243 A058139 A101476

Adjacent sequences: A151235 A151236 A151237 * A151239 A151240 A151241

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved