%I #14 Jan 11 2024 09:40:08

%S 1,3,7,11,19,23,31,39,55,59,67,75,91,99,115,131,163,167,175,183,199,

%T 207,223,239,271,279,295,311,343,359,391,423,487,491,499,507,523,531,

%U 547,563,595,603,619,635,667,683,715,747,811,819,835,851,883,899,931,963

%N a(n) = 2*A006046(n) + 1.

%C The number of edges in A080973-trees.

%C Conjectured partial sums of A131136. - _Sean A. Irvine_, Jun 25 2022

%H Michael De Vlieger, <a href="/A080978/b080978.txt">Table of n, a(n) for n = 0..10000</a>

%H Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, pp. 6, 30.

%t Map[2 # + 1 &, {0}~Join~Accumulate@ Map[Count[#, _?OddQ] &, Table[Binomial[n, k], {n, 0, 54}, {k, 0, n}]]] (* _Michael De Vlieger_, Oct 30 2022 *)

%Y Cf. A006046, A080973.

%K nonn

%O 0,2

%A _Antti Karttunen_, Mar 02 2003