A110201 a(n) = sum of squares of numbers < 2^n having exactly [n/2]+1 ones in their binary expansion.

1, 9, 70, 535, 3906, 29274, 215900, 1628175, 12197570, 92830430, 704127060, 5400199350, 41331491124, 318871044756, 2456608834680, 19039140186495, 147401590706370, 1146463189301430, 8909683732878500, 69495629981713650

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..20.

Formula

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

Mathematica

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 *)

Prog

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

Crossrefs

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

Sequence in context: A275680 A167534 A110202 * A045739 A098205 A000899

Adjacent sequences: A110198 A110199 A110200 * A110202 A110203 A110204

Keyword

nonn

Author

Paul D. Hanna, Jul 16 2005

Status

approved