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 A224513 Gray code variant of A147562. 2
 1, 5, 17, 21, 33, 69, 81, 85, 97, 133, 241, 277, 289, 325, 337, 341, 353, 389, 497, 533, 641, 965, 1073, 1109, 1121, 1157, 1265, 1301, 1313, 1349, 1361, 1365, 1377, 1413, 1521, 1557, 1665, 1989, 2097, 2133, 2241, 2565, 3537, 3861, 3969, 4293, 4401, 4437, 4449 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. 2^n-th terms = A002450 =(1, 5, 21, 85, 341, ...); as in A147562. At the date of this submission, it's unknown if the terms represent a simple CA rule for the numbers of ON cells. LINKS Table of n, a(n) for n=0..48. FORMULA For n>0, a(n) = 1 + 4 * Sum_{k=1..n} 3^(gt(k)-1) where gt() = A005811. Partial sums of A224512. EXAMPLE a(4) = 21 = (1 + 4 + 12 + 4), where (1, 4, 12, 4, ...) are the first four terms of A224512. PROG (PARI) gt(n) = sum(kk=1, n, (-1)^((kk/2^valuation(kk, 2)-1)/2)); \\ from A005811. a(n) = if (n==0, 1, 1 + 4*sum(k=1, n, 3^(gt(k)-1))); \\ Michel Marcus, Apr 22 2013 CROSSREFS Cf. A224512, A147562, A002450. Sequence in context: A351176 A211423 A211426 * A302423 A305478 A262620 Adjacent sequences: A224510 A224511 A224512 * A224514 A224515 A224516 KEYWORD nonn AUTHOR Gary W. Adamson, Apr 08 2013 STATUS approved

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Last modified May 29 02:26 EDT 2023. Contains 363029 sequences. (Running on oeis4.)