A110202 a(n) = sum of squares of numbers < 2^n having exactly 2 ones in their binary representation.

0, 9, 70, 395, 1984, 9429, 43434, 196095, 872788, 3842729, 16773118, 72693075, 313158312, 1342144509, 5726557522, 24338016935, 103078952956, 435222828369, 1832518331046, 7696579297275, 32252336887120, 134873417951909

Offset: 1

Author

Paul D. Hanna, Jul 16 2005

Keywords

• nonn

Comments

Equals column 2 of triangle A110200.

Examples

			For n=4, the sum of the squares of numbers < 2^4
having exactly 2 ones in their binary digits is:
a(4) = 3^2 + 5^2 + 6^2 + 9^2 + 10^2 + 12^2 = 395.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A110200 (triangle), A110201 (central terms), A002450 (column 1), A110203 (column 3), A110204 (column 4), A018900.

Programs

Mathematica

nn=30;With[{c=Union[FromDigits[#,2]&/@(Flatten[Table[Join[ {1},#]&/@ Permutations[Join[{1},PadRight[{},n,0]]],{n,0,nn}],1])]}, Table[ Total[ Select[c,#<2^n&]^2],{n,nn}]] (* Harvey P. Dale, Jan 27 2013 *)

PARI

a(n)=polcoeff(x^2*(9-38*x+32*x^2)/((1-x)^2*(1-2*x)*(1-4*x)^2+x*O(x^n)),n)

Formula

G.f.: x^2*(9-38*x+32*x^2)/( (1-x)^2*(1-2*x)*(1-4*x)^2 ). a(n) = Sum_{k|A018900(k)<2^n} A018900(k)^2.