A288599 a(n) = 2*a(n-1) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 10, a(4) = 16.

2, 4, 6, 10, 16, 28, 50, 90, 164, 300, 550, 1010, 1856, 3412, 6274, 11538, 21220, 39028, 71782, 132026, 242832, 446636, 821490, 1510954, 2779076, 5111516, 9401542, 17292130, 31805184, 58498852, 107596162, 197900194, 363995204, 669491556, 1231386950

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, 10->1000, starting with 00; see A288596.

Links

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

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

Formula

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

Mathematica

Join[{2}, LinearRecurrence[{2, 0, 0, -1}, {4, 6, 10, 16}, 40]]

Crossrefs

Cf. A288596.

Sequence in context: A160444 A158422 A018161 * A067880 A059749 A334213

Adjacent sequences: A288596 A288597 A288598 * A288600 A288601 A288602

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2017

Status

approved