A110201 - OEIS

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

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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