A288206 a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 18.

2, 4, 8, 18, 38, 80, 164, 334, 674, 1356, 2720, 5450, 10910, 21832, 43676, 87366, 174746, 349508, 699032, 1398082, 2796182, 5592384, 11184788, 22369598, 44739218, 89478460, 178956944, 357913914, 715827854, 1431655736, 2863311500, 5726623030, 11453246090

Offset

0,1

Comments

Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0010, 1->010, starting with 00; see A288203.

See the Comments of A288203 for a proof of this conjecture. - Michel Dekking, Oct 12 2018

Links

Clark Kimberling, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (3, -1, -3, 2).

Formula

a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 18.

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

a(n) = (-3 + (-1)^(1+n) + 2^(4+n) - 6*n) / 6. - Colin Barker, Sep 29 2017

Mathematica

LinearRecurrence[{3, -1, -3, 2}, {2, 4, 8, 18}, 40]

Prog

(PARI) Vec(2*(1 - x - x^2 + 2*x^3) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Sep 29 2017

Crossrefs

Cf. A288203.

Sequence in context: A024415 A339158 A220839 * A371791 A218078 A110110

Adjacent sequences: A288203 A288204 A288205 * A288207 A288208 A288209

Keyword

nonn,easy

Author

Clark Kimberling, Jun 07 2017

Status

approved