A059937 Sum of binary numbers with n 1's and two (possibly leading) 0's.

0, 7, 45, 186, 630, 1905, 5355, 14308, 36828, 92115, 225225, 540606, 1277874, 2981797, 6881175, 15728520, 35651448, 80215911, 179306325, 398458690, 880803630, 1937768217, 4244635395, 9261022956, 20132658900, 43620761275

Offset: 0

Author

Henry Bottomley, Feb 13 2001

Keywords

• nonn
• easy

Examples

			a(2) = 45 since binary sum of 1100 + 1010 + 1001 + 0110 + 0101 + 0011 is 12 + 10 + 9 + 6 + 5 + 3 = 45.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).

Crossrefs

Cf. A059672, A059673, A059938.

Programs

PARI

concat(0, Vec(x*(12*x^2-18*x+7)/((x-1)^3*(2*x-1)^3) + O(x^100))) \\ Colin Barker, Sep 13 2014

Formula

a(n) = (2^(n+2) - 1)*n*(n+1)/2 = A059672(n) + A059938(n) = a(n-1)*2*(n+1)/(n-1) + n(n+1)/2.

G.f.: x*(12*x^2-18*x+7) / ((x-1)^3*(2*x-1)^3). - Colin Barker, Sep 13 2014