A289107 a(n) = 2*a(n-1) - a(n-3) for n >= 5, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 22.

2, 4, 7, 12, 22, 37, 62, 102, 167, 272, 442, 717, 1162, 1882, 3047, 4932, 7982, 12917, 20902, 33822, 54727, 88552, 143282, 231837, 375122, 606962, 982087, 1589052, 2571142, 4160197, 6731342, 10891542, 17622887, 28514432, 46137322, 74651757, 120789082

Offset

0,1

Comments

Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->0010, 01->011, 10->000, starting with 00; see A289104.

Links

Clark Kimberling, Table of n, a(n) for n = 0..3000

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

Formula

a(n) = 2*a(n-1) - a(n-3) for n >= 5, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 22.

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

a(n) = -3 + 2^(-1-n)*sqrt(5)*(-(1-sqrt(5))^(1 + n) + (1+sqrt(5))^(1+n)) for n>1. - Colin Barker, Jun 28 2017

Mathematica

Join[{2, 4}, LinearRecurrence[{2, 0, -1}, {7, 12, 22}, 40]]

Crossrefs

Cf. A289104.

Sequence in context: A274174 A089259 A309733 * A221944 A257932 A287439

Adjacent sequences: A289104 A289105 A289106 * A289108 A289109 A289110

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved