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A173593 Numbers having in binary representation exactly two ones in three consecutive digits. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 9 16:32 EDT 2021. Contains 343742 sequences. (Running on oeis4.)