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->110, starting with 00; see A288306.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (2, 2, -3).
FORMULA
a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8.
G.f.: -((2*(-1 + 2*x^2))/(1 - 2*x - 2*x^2 + 3*x^3)).
a(n) = (2^(1-n)*(13*2^n + (13-4*sqrt(13))*(1-sqrt(13))^n + (1+sqrt(13))^n*(13+4*sqrt(13)))) / 39. - Colin Barker, Jun 09 2017
MATHEMATICA
LinearRecurrence[{2, 2, -3}, {2, 4, 8}, 40]
PROG
(PARI) Vec(2*(1 - 2*x^2) / ((1 - x)*(1 - x - 3*x^2)) + O(x^30)) \\ Colin Barker, Jun 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 09 2017
STATUS
approved