OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
M. Bousquet-Mélou, M. Petkovsek, Walks confined in a quadrant are not always D-finite, Theoretical Computer Science, 307(2003): 257-276.
Ira M. Gessel, A probabilistic method for lattice path enumeration, Journal of statistical planning and inference, 14 (1986), 49-58.
FORMULA
a(n) ~ c * (27/4)^n / n^(3/2), where c = 0.06045583689606517807688682344735167414726208387456561322459238109992522838... . - Vaclav Kotesovec, Oct 07 2016
MAPLE
b:= proc(l) option remember; `if`(l=[1$2], 1, add((p->
`if`(p[1]<0, 0, b(p)))(sort((l-x))), x=[[-1, 2], [2, -1]]))
end:
a:= n-> b([0, 3*n]):
seq(a(n), n=1..30); # Alois P. Heinz, Oct 06 2016
MATHEMATICA
b[l_List] := b[l] = If[l == {1, 1}, 1, Sum[Function[p, If[p[[1]]<0, 0, b[p]]][Sort[l-x]], {x, {{-1, 2}, {2, -1}}}]]; a[n_] := b[{0, 3n}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Dec 04 2016 after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Feng Jishe, Oct 06 2016
EXTENSIONS
More terms from Alois P. Heinz, Oct 06 2016
STATUS
approved