A224513 Gray code variant of A147562.

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

Offset: 0

Author

Gary W. Adamson, Apr 08 2013

Keywords

• nonn

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.

Examples

			a(4) = 21 = (1 + 4 + 12 + 4), where (1, 4, 12, 4, ...) are the first four terms of A224512.
		

Crossrefs

Cf. A224512, A147562, A002450.

Programs

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

Formula

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

Partial sums of A224512.