cp's OEIS Frontend

A048116 a(n) = T(2n,n), where T is given by A048113.

%I A048116 #27 Oct 19 2020 03:42:48
%S A048116 1,2,4,12,36,120,408,1440,5160,18816,69336,258048,967344,3649536,
%T A048116 13839504,52715952,201556944,773182608,2974442112,11471570352,
%U A048116 44341125312,171732665520,666302137056,2589317125824,10076939895984,39268487472336,153208051192848
%N A048116 a(n) = T(2n,n), where T is given by A048113.
%C A048116 Number of planar walks starting at (1,1), ending at (n,n), remaining in the first quadrant and using steps (-1,2) and (2,-1).
%H A048116 Alois P. Heinz, <a href="/A048116/b048116.txt">Table of n, a(n) for n = 1..1000</a>
%H A048116 M. Bousquet-Mélou and M. Petkovsek, <a href="http://arXiv.org/abs/math.CO/0211432">Walks confined in a quadrant are not always D-finite</a>
%F A048116 a(n) ~ c * 4^n / sqrt(n), where c = 0.03748220353529780423030694970938451772844604409392271... . - _Vaclav Kotesovec_, Oct 07 2016
%p A048116 b:= proc(l) option remember; `if`(l=[1$2], 1, add((p->
%p A048116       `if`(p[1]<0, 0, b(p)))(sort(l-x)), x=[[-1, 2], [2, -1]]))
%p A048116     end:
%p A048116 a:= n-> b([n$2]):
%p A048116 seq(a(n), n=1..30);  # _Alois P. Heinz_, Oct 06 2016
%t A048116 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[{n, n}]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Dec 02 2016 after _Alois P. Heinz_ *)
%Y A048116 Cf. A048113, A277262.
%K A048116 nonn,walk
%O A048116 1,2
%A A048116 _Clark Kimberling_
%E A048116 a(1)=1 prepended by _Alois P. Heinz_, Oct 06 2016