This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A088564 #13 Jul 01 2025 19:27:59
%S A088564 1,3,3,5,6,6,6,6,6,8,9,9,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,
%T A088564 14,15,15,16,18,18,18,18,18,19,21,21,23,24,24,24,24,24,24,24,24,24,24,
%U A088564 24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24
%N A088564 a(n)=sum(i=0,n,binomial(2*i,i) (mod 3)).
%C A088564 Distinct values (i.e. 1,3,5,6,8,9,...) are given by the partial sums of the Thue-Morse sequence on alphabet (1,2) A026430. Sequence of least k such that a(k)>a(k-1) is given by A005836. For any k>=0, card{ n : a(3*A005836(k)) =a(n)}=1.
%C A088564 Only 79 of the first 1001 terms are odd numbers. -- From _Harvey P. Dale_, Aug 08 2012
%H A088564 Harvey P. Dale, <a href="/A088564/b088564.txt">Table of n, a(n) for n = 0..1000</a>
%t A088564 Table[Sum[Mod[Binomial[2*i,i],3],{i,0,n}],{n,0,80}] (* _Harvey P. Dale_, Aug 08 2012 *)
%Y A088564 Cf. A001285, A005836, A006996.
%K A088564 nonn
%O A088564 0,2
%A A088564 _Benoit Cloitre_, Nov 19 2003