A110201 - OEIS

%I #6 Aug 22 2021 19:29:44

%S 1,9,70,535,3906,29274,215900,1628175,12197570,92830430,704127060,

%T 5400199350,41331491124,318871044756,2456608834680,19039140186495,

%U 147401590706370,1146463189301430,8909683732878500,69495629981713650

%N a(n) = sum of squares of numbers < 2^n having exactly [n/2]+1 ones in their binary expansion.

%C a(n) equals the largest term in row n of triangle A110200.

%F a(n) = (4^n-1)/3*C(n-2, n\2) + (2^n-1)^2*C(n-2, n\2-1).

%t Join[{1},Table[Total[Select[Range[2^n],DigitCount[#,2,1]==Floor[ n/2]+ 1&]^2],{n,2,20}]] (* _Harvey P. Dale_, Aug 22 2021 *)

%o (PARI) a(n)=(4^n-1)/3*binomial(n-2,n\2)+(2^n-1)^2*binomial(n-2,n\2-1)

%Y Cf. A110200 (triangle), A002450 (column 1), A110202 (column 2), A110203 (column 3), A110204 (column 4).

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jul 16 2005