A110203 a(n) = sum of squares of numbers < 2^n having exactly 3 ones in their binary representation.

0, 0, 49, 535, 3906, 24066, 135255, 717825, 3662848, 18158932, 88043517, 419348475, 1968346446, 9126412278, 41875079155, 190408381765, 858989527020, 3848282308584, 17134038373689, 75866264567775, 334251455152090

Offset: 1

Author

Paul D. Hanna, Jul 16 2005

Keywords

• nonn

Comments

Equals column 3 of triangle A110200.

Examples

			For n=4, the sum of the squares of numbers < 2^4
having exactly 3 ones in their binary digits is:
a(4) = 7^2 + 11^2 + 13^2 + 14^2 = 535.
		

Crossrefs

Cf. A110200 (triangle), A110201 (central terms), A002450 (column 1), A110202 (column 2), A110204 (column 4).

Programs

PARI

{a(n)=polcoeff(x^3*(49-396*x+1140*x^2-1360*x^3+576*x^4)/ ((1-x)^3*(1-2*x)^2*(1-4*x)^3+x*O(x^n)),n)}

Formula

G.f.: x^3*(49-396*x+1140*x^2-1360*x^3+576*x^4)/((1-x)^3*(1-2*x)^2*(1-4*x)^3).