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%I #14 Feb 18 2018 03:43:05
%S 3,5,6,11,13,22,27,45,54,91,109,182,219,365,438,731,877,1462,1755,
%T 2925,3510,5851,7021,11702,14043,23405,28086,46811,56173,93622,112347,
%U 187245,224694,374491,449389,748982,898779,1497965,1797558,2995931,3595117
%N Numbers having in binary representation exactly two ones in three consecutive digits.
%C a(2*n-1) = A033129(n+1);
%C a(3*n-2) = A113836(n+1);
%C a(6*n-5) = A083713(n);
%C a(2*n) - a(2*n-1) = A077947(n+1);
%C a(2*n+1) - a(2*n) = A077947(n).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 1, 0, -2).
%F From _R. J. Mathar_, Feb 24 2010: (Start)
%F a(n) = 2*a(n-2) + a(n-3) - 2*a(n-5).
%F G.f.: x*(-3-5*x+2*x^3+4*x^4)/ ((1-x) * (1+x+x^2) * (2*x^2-1)). (End)
%e a(10) = 91 = 1011011_2
%e a(11) = 109 = 1101101_2
%e a(12) = 182 = 10110110_2
%e a(13) = 219 = 11011011_2
%e a(14) = 365 = 101101101_2
%e a(15) = 438 = 110110110_2
%e a(16) = 731 = 1011011011_2
%e a(17) = 877 = 1101101101_2
%e a(18) = 1462 = 10110110110_2
%e a(19) = 1755 = 11011011011_2
%e a(20) = 2925 = 101101101101_2
%t LinearRecurrence[{0, 2, 1, 0, -2}, {3, 5, 6, 11, 13}, 50] (* _Jean-François Alcover_, Feb 17 2018 *)
%Y Cf. A007088.
%Y Bisections A033129, A033120.
%K nonn,base,easy
%O 1,1
%A _Reinhard Zumkeller_, Feb 22 2010
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