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A048116
a(n) = T(2n,n), where T is given by A048113.
4
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
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
Sequence in context: A245798 A241530 A123071 * A148209 A148210 A148211
KEYWORD
nonn,walk
EXTENSIONS
a(1)=1 prepended by Alois P. Heinz, Oct 06 2016
STATUS
approved