A227326 - OEIS

%I #7 Jul 08 2013 10:14:58

%S 0,2,8,8,32,32,80,128,320,512,1088,2048,4256,8192,16640,32768,66176,

%T 131072,263168,524288,1050752,2097152,4198400,8388608,16785728,

%U 33554432,67125248,134217728,268468736,536870912,1073807360,2147483648,4295099648,8589934592

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

%C 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).

%H Reinhard Zumkeller, <a href="/A227326/b227326.txt">Table of n, a(n) for n = 0..1000</a>

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

%o (PARI) a(n)=sum(k=0,valuation(n,2),2^(k+n/2^k))

%o (PARI) a(n)=if(n<1,0,if(n%2==0,2*a(n/2)+2^n,2^n))

%o (Haskell)

%o import Data.List (transpose)

%o a227326 n = a227326_list !! n

%o a227326_list = 0 : xs where

%o    xs = concat $ transpose

%o         [a004171_list, zipWith (+) (tail a000302_list) (map (* 2) xs)]

%o -- _Reinhard Zumkeller_, Jul 08 2013

%Y Cf. A000302, A004171.

%K nonn,easy

%O 0,2

%A _Ralf Stephan_, Jul 07 2013