A213673 - OEIS

%I #34 Aug 22 2013 15:58:30

%S 0,0,0,1,0,2,4,7,0,4,8,13,16,22,28,35,0,8,16,25,32,42,52,63,64,76,88,

%T 101,112,126,140,155,0,16,32,49,64,82,100,119,128,148,168,189,208,230,

%U 252,275,256,280,304,329,352,378,404,431,448,476,504

%N (n^2 - A000695(n))/4.

%C A000695 is a 'pseudo-square function' that takes the binary expansion of n and moves bit k to bit 2k (that is, towards the most significant bits).

%C a(n) = 0 if and only if n is 0 or a power of 2.

%H R. J. Mathar, <a href="/A213673/b213673.txt">Table of n, a(n) for n = 0..1023</a>

%e For example 7 = 111, and PSF(7) = 10101 = 21, so a(7) = (49 - 21)/4 = 7.

%e 13 = 1101 -> 1010001 = 81, so a(13) = (169 - 81)/4 = 22.

%o (PARI) a(n)=my(v=binary(n));(n^2-sum(i=1,#v,v[i]*4^(#v-i)))/4 \\ _Charles R Greathouse IV_, Mar 04 2013

%Y Cf. A000290, A000695.

%K nonn

%O 0,6

%A _Jon Perry_, Mar 03 2013