A059938 Sum of binary numbers with n 1's and two (non-leading) 0's.

0, 4, 31, 141, 506, 1590, 4593, 12523, 32740, 82908, 204755, 495561, 1179582, 2768818, 6422437, 14745495, 33554312, 75759480, 169869159, 378535765, 838860610, 1849687854, 4060086041, 8875147011, 19327352556, 41943039700

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) = n^2*2^(n+1) - n*(n-1)/2 = A059937(n) - A059672(n) = A059937(n-1) + 2^(n+1)*n*(n+1)/2.

G.f.: x*(8*x^3-6*x^2-5*x+4) / ((x-1)^3*(2*x-1)^3). - Colin Barker, Sep 14 2014

Example

a(2) = 1100_2 + 1010_2 + 1001_2 = 12 + 10 + 9 = 31.

Prog

(PARI) concat(0, Vec(x*(8*x^3-6*x^2-5*x+4)/((x-1)^3*(2*x-1)^3) + O(x^100))) \\ Colin Barker, Sep 14 2014

Crossrefs

Cf. A059672, A059673, A059937.

Sequence in context: A297501 A296734 A220284 * A263761 A263762 A263763

Adjacent sequences: A059935 A059936 A059937 * A059939 A059940 A059941

Keyword

nonn,easy

Author

Henry Bottomley, Feb 13 2001

Status

approved