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A244224 a(n) = Number of nonnegative integers 0 <= k <= n, which have an even representation in Greedy Catalan Base (A014418).

%I A244224 #7 Jun 25 2014 13:12:09
%S A244224 1,1,2,2,3,4,4,5,5,6,7,7,8,8,9,9,10,10,11,12,12,13,13,14,15,15,16,16,
%T A244224 17,17,18,18,19,20,20,21,21,22,23,23,24,24,25,25,26,26,27,28,28,29,29,
%U A244224 30,31,31,32,32,33,33,34,34,35,36,36,37,37,38,39,39,40,40,41,41,42,42
%N A244224 a(n) = Number of nonnegative integers 0 <= k <= n, which have an even representation in Greedy Catalan Base (A014418).
%C A244224 The terms a(0) .. a(23) are equal to A076905(1) .. A076905(24).
%H A244224 Antti Karttunen, <a href="/A244224/b244224.txt">Table of n, a(n) for n = 0..4862</a>
%e A244224 The first nonnegative integers represented in Greedy Catalan Base look like this:
%e A244224 A014418(0) = 0
%e A244224 A014418(1) = 1
%e A244224 A014418(2) = 10
%e A244224 A014418(3) = 11
%e A244224 A014418(4) = 20
%e A244224 A014418(5) = 100
%e A244224 A014418(6) = 101
%e A244224 A014418(7) = 110
%e A244224 Of these, the first "even" representation (ending with zero) occurs at n=0, thus a(0) = 1, and as 1 is odd, also a(1) = 1. The next even occurs at n=2, so a(2) = 2. The next even representations after that occur at n=4, 5 and 7, thus a(3) = 2, a(4) = 3, a(5) = 4, a(6) = 4 and a(7) = 5.
%o A244224 (Scheme, with _Antti Karttunen_'s IntSeq-library for memoizing definec-macro)
%o A244224 (definec (A244224 n) (if (zero? n) 1 (+ (A244220 n) (A244224 (- n 1)))))
%Y A244224 Partial sums of A244220.
%Y A244224 One more than A244229.
%Y A244224 Cf. A244225, A076905.
%K A244224 nonn
%O A244224 0,3
%A A244224 _Antti Karttunen_, Jun 23 2014