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

1,3

Comments

Equals column 3 of triangle A110200.

Links

Table of n, a(n) for n=1..21.

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).

Example

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.

Prog

(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)}

Crossrefs

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

Sequence in context: A337356 A030510 A104935 * A263704 A166832 A299711

Adjacent sequences: A110200 A110201 A110202 * A110204 A110205 A110206

Keyword

nonn

Author

Paul D. Hanna, Jul 16 2005

Status

approved