A048116 a(n) = T(2n,n), where T is given by A048113.
1, 2, 4, 12, 36, 120, 408, 1440, 5160, 18816, 69336, 258048, 967344, 3649536, 13839504, 52715952, 201556944, 773182608, 2974442112, 11471570352, 44341125312, 171732665520, 666302137056, 2589317125824, 10076939895984, 39268487472336, 153208051192848
Offset: 1
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
- M. Bousquet-Mélou and M. Petkovsek, Walks confined in a quadrant are not always D-finite
Programs
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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([n$2]): 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[{n, n}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Dec 02 2016 after Alois P. Heinz *)
Formula
a(n) ~ c * 4^n / sqrt(n), where c = 0.03748220353529780423030694970938451772844604409392271... . - Vaclav Kotesovec, Oct 07 2016
Extensions
a(1)=1 prepended by Alois P. Heinz, Oct 06 2016
Comments