A288260 a(n) = 2*a(n-1) + 2*a(n-3) - 3*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16.

2, 4, 8, 16, 34, 72, 152, 324, 690, 1468, 3128, 6664, 14194, 30240, 64424, 137244, 292386, 622900, 1327016, 2827072, 6022786, 12830904, 27334904, 58234164, 124061778, 264300652, 563064920, 1199550904, 2555517778, 5444263440, 11598433928, 24709250700

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->100, starting with 00; see A288257. [Mapping corrected by Michel Dekking, Mar 05 2020.]

Second Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0101, 1->`010, starting with 00; see A288466. - Michel Dekking, Mar 05 2020

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,0,2,-3).

Formula

a(n) = 2*a(n-1) + 2*a(n-3) - 3*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16.

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

Mathematica

LinearRecurrence[{2, 0, 2, -3}, {2, 4, 8, 16}, 40]

Crossrefs

Cf. A288257, A288466.

Sequence in context: A088325 A215930 A367660 * A006210 A288176 A096812

Adjacent sequences: A288257 A288258 A288259 * A288261 A288262 A288263

Keyword

nonn,easy

Author

Clark Kimberling, Jun 09 2017

Status

approved