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->00, starting with 00; see A288106.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (0, 3, 1, 0, 1, 0, -3, -1).
FORMULA
a(n) = 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) - a(n-7), where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 14, a(4) = 25, a(5) = 47, a(6) = 88, a(7) = 166.
G.f.: (2 + 4*x + x^2 - 4*x^5 - 5*x^6 - x^7)/(1 - 3*x^2 - x^3 - x^5 + 3*x^7 + x^8).
MATHEMATICA
LinearRecurrence[{0, 3, 1, 0, 1, 0, -3, -1}, {2, 4, 7, 14, 25, 47, 88, 166}, 40]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 06 2017
STATUS
approved