cp's OEIS Frontend

A173593 Numbers having in binary representation exactly two ones in three consecutive digits.

%I A173593 #14 Feb 18 2018 03:43:05
%S A173593 3,5,6,11,13,22,27,45,54,91,109,182,219,365,438,731,877,1462,1755,
%T A173593 2925,3510,5851,7021,11702,14043,23405,28086,46811,56173,93622,112347,
%U A173593 187245,224694,374491,449389,748982,898779,1497965,1797558,2995931,3595117
%N A173593 Numbers having in binary representation exactly two ones in three consecutive digits.
%C A173593 a(2*n-1) = A033129(n+1);
%C A173593 a(3*n-2) = A113836(n+1);
%C A173593 a(6*n-5) = A083713(n);
%C A173593 a(2*n) - a(2*n-1) = A077947(n+1);
%C A173593 a(2*n+1) - a(2*n) = A077947(n).
%H A173593 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 1, 0, -2).
%F A173593 From _R. J. Mathar_, Feb 24 2010: (Start)
%F A173593 a(n) = 2*a(n-2) + a(n-3) - 2*a(n-5).
%F A173593 G.f.: x*(-3-5*x+2*x^3+4*x^4)/ ((1-x) * (1+x+x^2) * (2*x^2-1)). (End)
%e A173593 a(10) =   91 =      1011011_2
%e A173593 a(11) =  109 =      1101101_2
%e A173593 a(12) =  182 =     10110110_2
%e A173593 a(13) =  219 =     11011011_2
%e A173593 a(14) =  365 =    101101101_2
%e A173593 a(15) =  438 =    110110110_2
%e A173593 a(16) =  731 =   1011011011_2
%e A173593 a(17) =  877 =   1101101101_2
%e A173593 a(18) = 1462 =  10110110110_2
%e A173593 a(19) = 1755 =  11011011011_2
%e A173593 a(20) = 2925 = 101101101101_2
%t A173593 LinearRecurrence[{0, 2, 1, 0, -2}, {3, 5, 6, 11, 13}, 50] (* _Jean-François Alcover_, Feb 17 2018 *)
%Y A173593 Cf. A007088.
%Y A173593 Bisections A033129, A033120.
%K A173593 nonn,base,easy
%O A173593 1,1
%A A173593 _Reinhard Zumkeller_, Feb 22 2010