A088564 - OEIS

%I #13 Jul 01 2025 19:27:59

%S 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 14,15,15,16,18,18,18,18,18,19,21,21,23,24,24,24,24,24,24,24,24,24,24,

%U 24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24

%N a(n)=sum(i=0,n,binomial(2*i,i) (mod 3)).

%C 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 Only 79 of the first 1001 terms are odd numbers.  -- From _Harvey P. Dale_, Aug 08 2012

%H Harvey P. Dale, <a href="/A088564/b088564.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[Sum[Mod[Binomial[2*i,i],3],{i,0,n}],{n,0,80}] (* _Harvey P. Dale_, Aug 08 2012 *)

%Y Cf. A001285, A005836, A006996.

%K nonn

%O 0,2

%A _Benoit Cloitre_, Nov 19 2003