A288476 a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8.

2, 4, 8, 20, 44, 108, 244, 588, 1348, 3212, 7428, 17580, 40868, 96332, 224644, 528236, 1234148, 2897804, 6777924, 15900844, 37216932, 87264460, 204330500, 478954476, 1121747556, 2628904460, 6157985732, 14430108460, 33804242468, 79208704844, 185565457796

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->011, starting with 00; see A288473.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1, 4, -2).

Formula

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

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

Mathematica

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

Crossrefs

Cf. A288473.

Sequence in context: A105319 A051389 A078006 * A338197 A056952 A369496

Adjacent sequences: A288473 A288474 A288475 * A288477 A288478 A288479

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2017

Status

approved