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

1,2

Comments

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).

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

Formula

a(n) ~ c * 4^n / sqrt(n), where c = 0.03748220353529780423030694970938451772844604409392271... . - 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([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 *)

Crossrefs

Cf. A048113, A277262.

Sequence in context: A245798 A241530 A123071 * A148209 A148210 A148211

Adjacent sequences: A048113 A048114 A048115 * A048117 A048118 A048119

Keyword

nonn,walk

Author

Clark Kimberling

Extensions

a(1)=1 prepended by Alois P. Heinz, Oct 06 2016

Status

approved