A213673 (n^2 - A000695(n))/4.

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, 101, 112, 126, 140, 155, 0, 16, 32, 49, 64, 82, 100, 119, 128, 148, 168, 189, 208, 230, 252, 275, 256, 280, 304, 329, 352, 378, 404, 431, 448, 476, 504

Offset

0,6

Comments

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).

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

Links

R. J. Mathar, Table of n, a(n) for n = 0..1023

Example

For example 7 = 111, and PSF(7) = 10101 = 21, so a(7) = (49 - 21)/4 = 7.
13 = 1101 -> 1010001 = 81, so a(13) = (169 - 81)/4 = 22.

Prog

(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

Crossrefs

Cf. A000290, A000695.

Sequence in context: A111768 A011177 A335534 * A118946 A097879 A180658

Adjacent sequences: A213670 A213671 A213672 * A213674 A213675 A213676

Keyword

nonn

Author

Jon Perry, Mar 03 2013

Status

approved