OFFSET
0,1
COMMENTS
Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->0010, 01->011, 10->100, starting with 00; see A289057.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,2,1,-2,1).
FORMULA
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 2*a(n-4) + a(n-5) -2*a(n-6) + a(n-7) for n >= 7, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 30, a(6) = 47.
G.f.: (-2 + 3*x^2 - x^3 - x^4 - x^5 + x^6 + x^7 - 2*x^8 + x^9)/((-1 + x)^2*(-1 + 2*x^2 + x^5)).
MATHEMATICA
Join[{2, 4, 7}, LinearRecurrence[{2, 1, -4, 2, 1, -2, 1}, {11, 18, 30, 47, 74, 114, 176}, 40]]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 28 2017
STATUS
approved