A288603 a(n) = 2*a(n-1) - a(n-3) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 8.

2, 4, 6, 8, 12, 18, 28, 44, 70, 112, 180, 290, 468, 756, 1222, 1976, 3196, 5170, 8364, 13532, 21894, 35424, 57316, 92738, 150052, 242788, 392838, 635624, 1028460, 1664082, 2692540, 4356620, 7049158, 11405776, 18454932, 29860706, 48315636, 78176340, 126491974

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->0101, 1->1001, starting with 00; see A288600.

Links

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

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

Formula

a(n) = 2*a(n-1) - a(n-3) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 8.

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

a(n) = Fibonacci(n) + Lucas(n) + 2 for n >= 1. - Greg Dresden, Oct 10 2020

Mathematica

Join[{2}, LinearRecurrence[{2, 0, -1}, {4, 6, 8}, 40]]

Crossrefs

Cf. A288600.

Sequence in context: A015897 A240211 A050597 * A324939 A057335 A126907

Adjacent sequences: A288600 A288601 A288602 * A288604 A288605 A288606

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2017

Status

approved