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

1,2

Comments

Equals column 2 of triangle A110200.

Links

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

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.

Example

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.

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 *)

Prog

(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)

Crossrefs

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

Sequence in context: A193706 A275680 A167534 * A110201 A045739 A098205

Adjacent sequences: A110199 A110200 A110201 * A110203 A110204 A110205

Keyword

nonn

Author

Paul D. Hanna, Jul 16 2005

Status

approved