A227326 a(2n) = 2a(n)+2^(2n), a(2n+1) = 2^(2n+1), a(0)=0.

0, 2, 8, 8, 32, 32, 80, 128, 320, 512, 1088, 2048, 4256, 8192, 16640, 32768, 66176, 131072, 263168, 524288, 1050752, 2097152, 4198400, 8388608, 16785728, 33554432, 67125248, 134217728, 268468736, 536870912, 1073807360, 2147483648, 4295099648, 8589934592

Offset

0,2

Comments

Simplest sequence of form a(2n)=c*a(n)+f(n), a(2n+1)=g(n) that cannot be easily expressed as a function of A007814(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Formula

a(n) = sum(k=0..A007814(n), 2^(k+n/2^k) ).

Prog

(PARI) a(n)=sum(k=0, valuation(n, 2), 2^(k+n/2^k))
(PARI) a(n)=if(n<1, 0, if(n%2==0, 2*a(n/2)+2^n, 2^n))
(Haskell)
import Data.List (transpose)
a227326 n = a227326_list !! n
a227326_list = 0 : xs where
   xs = concat $ transpose
        [a004171_list, zipWith (+) (tail a000302_list) (map (* 2) xs)]
-- Reinhard Zumkeller, Jul 08 2013

Crossrefs

Cf. A000302, A004171.

Sequence in context: A180825 A230708 A230739 * A323852 A064231 A181130

Adjacent sequences: A227323 A227324 A227325 * A227327 A227328 A227329

Keyword

nonn,easy

Author

Ralf Stephan, Jul 07 2013

Status

approved