

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
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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.
At the date of this submission, it's unknown if the terms represent a simple CA rule for the numbers of ON cells.


LINKS



FORMULA

For n>0, a(n) = 1 + 4 * Sum_{k=1..n} 3^(gt(k)1) where gt() = A005811.


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



KEYWORD

nonn


AUTHOR



STATUS

approved



