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%I #14 Feb 20 2022 15:11:55
%S 1,5,17,21,33,69,81,85,97,133,241,277,289,325,337,341,353,389,497,533,
%T 641,965,1073,1109,1121,1157,1265,1301,1313,1349,1361,1365,1377,1413,
%U 1521,1557,1665,1989,2097,2133,2241,2565,3537,3861,3969,4293,4401,4437,4449
%N Gray code variant of A147562.
%C A147562 = the partial sums of A147582, derived from the binary weight of n, wt() = A000120. A224513 = the partial sums of A224512, derived from the Gray code weight of n (number of 1's in the representation of n), gt() = A005811.
%C 2^n-th terms = A002450 =(1, 5, 21, 85, 341, ...); as in A147562.
%C At the date of this submission, it's unknown if the terms represent a simple CA rule for the numbers of ON cells.
%F For n>0, a(n) = 1 + 4 * Sum_{k=1..n} 3^(gt(k)-1) where gt() = A005811.
%F Partial sums of A224512.
%e a(4) = 21 = (1 + 4 + 12 + 4), where (1, 4, 12, 4, ...) are the first four terms of A224512.
%o (PARI) gt(n) = sum(kk=1, n, (-1)^((kk/2^valuation(kk, 2)-1)/2)); \\ from A005811.
%o a(n) = if (n==0, 1, 1 + 4*sum(k=1, n, 3^(gt(k)-1))); \\ _Michel Marcus_, Apr 22 2013
%Y Cf. A224512, A147562, A002450.
%K nonn
%O 0,2
%A _Gary W. Adamson_, Apr 08 2013
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