A110203 - OEIS

%I #3 Mar 30 2012 18:36:49

%S 0,0,49,535,3906,24066,135255,717825,3662848,18158932,88043517,

%T 419348475,1968346446,9126412278,41875079155,190408381765,

%U 858989527020,3848282308584,17134038373689,75866264567775,334251455152090

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

%C Equals column 3 of triangle A110200.

%F 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).

%e For n=4, the sum of the squares of numbers < 2^4

%e having exactly 3 ones in their binary digits is:

%e a(4) = 7^2 + 11^2 + 13^2 + 14^2 = 535.

%o (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)}

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

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jul 16 2005