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%I #16 Mar 09 2024 13:06:16
%S 0,4,31,141,506,1590,4593,12523,32740,82908,204755,495561,1179582,
%T 2768818,6422437,14745495,33554312,75759480,169869159,378535765,
%U 838860610,1849687854,4060086041,8875147011,19327352556,41943039700
%N Sum of binary numbers with n 1's and two (non-leading) 0's.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-33,63,-66,36,-8).
%F 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.
%F G.f.: x*(8*x^3-6*x^2-5*x+4) / ((x-1)^3*(2*x-1)^3). - _Colin Barker_, Sep 14 2014
%e a(2) = 1100_2 + 1010_2 + 1001_2 = 12 + 10 + 9 = 31.
%o (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
%Y Cf. A059672, A059673, A059937.
%K nonn,easy
%O 0,2
%A _Henry Bottomley_, Feb 13 2001
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