A288219 a(n) = a(n-1) + a(n-2) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 7.

2, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521, 87403803, 141422324

Offset: 0

Author

Clark Kimberling, Jun 19 2017

Keywords

• nonn
• easy

Comments

Empirically, a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->1000, 10->010, starting with 00; see A288216.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (1, 1).

Crossrefs

Cf. A288216, A163695, A080023, A000204.

Programs

Mathematica

Join[{2}, LinearRecurrence[{1, 1}, {4, 7}, 40]]

Formula

a(n) = a(n-1) + a(n-2) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 7.

a(n) = L(n+2) for n >=1, where L = A000032 (Lucas numbers).

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