A083942 Positions of breadth-first-wise encodings (A002542) of the complete binary trees (A084107) in A014486.

0, 1, 8, 625, 13402696, 19720133460129649, 126747521841153485025455279433135688, 15141471069096667541622192498608408980462133134430650704600552060872705905

Offset: 0

Author

Antti Karttunen, May 13 2003

Keywords

• nonn

Links

• Alexander Adamchuk, Nov 10 2007, Table of n, a(n) for n = 0..11
• Eric Weisstein's World of Mathematics, Catalan Number.

Crossrefs

Cf. A014138 (partial sums of Catalan numbers), A000108 (Catalan Numbers).

Formula

a(n) = A057118(A084108(n)).

a(n) = A080300(A002542(n)) [provided that 2^((2^n)-1)*((2^((2^n)-1))-1) is indeed the formula for A002542].

Conjecture: a(n) = A014138(2^n-2) for n>0. - Alexander Adamchuk, Nov 10 2007

Conjecture: a(n) = Sum_{k=1..2^n-1} A000108(k). - Alexander Adamchuk, Nov 10 2007

Let h(n) = -((C(2*n,n)*hypergeom([1,1/2+n],[2+n],4))/(1+n)+I*sqrt(3)/2+1/2). Assuming Adamchuk's conjecture a(n) = h(2^n) and A014138(n) = h(n+1). - Peter Luschny, Mar 09 2015