OFFSET
1,3
COMMENTS
A001453 is a subsequence. - Altug Alkan, Sep 29 2016
n>=1 is in the sequence if and only if there is a Catalan number c such that c/2 <= n < c and c-n-1 is in the sequence. - Robert Israel, Nov 20 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(i) + a(2^n+1-i) = A000108(n+1)-1 for 1<=i<=2^n. - Robert Israel, Nov 20 2016
EXAMPLE
3 is in the sequence because the permutation (1,3,2) added termwise to (1,2,3) yields (2,5,5) and both 2 and 5 are Catalan numbers.
MAPLE
S:= {0}:
for i from 1 to 8 do
c:= binomial(2*i, i)/(i+1);
S:= S union map(t -> c - t - 1, S);
od:
sort(convert(S, list)); # Robert Israel, Nov 20 2016
MATHEMATICA
CatalanTo[n0_] :=
Module[{n = n0}, k = 1; L = {};
While[CatalanNumber[k] <= 2*n, L = {L, CatalanNumber[k]}; k++];
L = Flatten[L]]
perms[n0_] := Module[{n = n0, S, func, T, T2},
func[k_] := Cases[CatalanTo[n], x_ /; 1 <= x - k <= n] - k;
T = Tuples[Table[func[k], {k, 1, n}]];
T2 = Cases[T, x_ /; Length[Union[x]] == Length[x]];
Length[T2]]
Select[Range[41], perms[#] > 0 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary E. Davis, Sep 24 2016
EXTENSIONS
More terms from Alois P. Heinz, Sep 28 2016
a(23)-a(58) from Robert Israel, Nov 18 2016
STATUS
approved