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

1,1

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).

Links

Table of n, a(n) for n=1..41.

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

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)

Example

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

Mathematica

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

Crossrefs

Cf. A007088.

Bisections A033129, A033120.

Sequence in context: A145714 A326310 A047443 * A268495 A127577 A280590

Adjacent sequences: A173590 A173591 A173592 * A173594 A173595 A173596

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Feb 22 2010

Status

approved