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

3, 5, 6, 11, 13, 22, 27, 45, 54, 91, 109, 182, 219, 365, 438, 731, 877, 1462, 1755, 2925, 3510, 5851, 7021, 11702, 14043, 23405, 28086, 46811, 56173, 93622, 112347, 187245, 224694, 374491, 449389, 748982, 898779, 1497965, 1797558, 2995931, 3595117

Offset: 1

Author

Reinhard Zumkeller, Feb 22 2010

Keywords

• nonn
• base
• easy

Comments

a(2*n-1) = A033129(n+1);

a(3*n-2) = A113836(n+1);

a(6*n-5) = A083713(n);

a(2*n) - a(2*n-1) = A077947(n+1);

a(2*n+1) - a(2*n) = A077947(n).

Examples

			a(10) =   91 =      1011011_2
a(11) =  109 =      1101101_2
a(12) =  182 =     10110110_2
a(13) =  219 =     11011011_2
a(14) =  365 =    101101101_2
a(15) =  438 =    110110110_2
a(16) =  731 =   1011011011_2
a(17) =  877 =   1101101101_2
a(18) = 1462 =  10110110110_2
a(19) = 1755 =  11011011011_2
a(20) = 2925 = 101101101101_2
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 2, 1, 0, -2).

Crossrefs

Cf. A007088.

Bisections A033129, A033120.

Programs

Mathematica

LinearRecurrence[{0, 2, 1, 0, -2}, {3, 5, 6, 11, 13}, 50] (* Jean-François Alcover, Feb 17 2018 *)

Formula

From R. J. Mathar, Feb 24 2010: (Start)

a(n) = 2*a(n-2) + a(n-3) - 2*a(n-5).

G.f.: x*(-3-5*x+2*x^3+4*x^4)/ ((1-x) * (1+x+x^2) * (2*x^2-1)). (End)