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A059937 Sum of binary numbers with n 1's and two (possibly leading) 0's. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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

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

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A059672, A059673, A059938.

Sequence in context: A208826 A206808 A197369 * A278682 A323140 A236194

Adjacent sequences:  A059934 A059935 A059936 * A059938 A059939 A059940

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Feb 13 2001

STATUS

approved

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Last modified February 27 04:40 EST 2021. Contains 341649 sequences. (Running on oeis4.)