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 A288219 a(n) = a(n-1) + a(n-2) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 7. 6
 2, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521, 87403803, 141422324 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Empirically, a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->1000, 10->010, starting with 00; see A288216. LINKS Clark Kimberling, Table of n, a(n) for n = 0..2000 Index entries for linear recurrences with constant coefficients, signature (1, 1). FORMULA a(n) = a(n-1) + a(n-2) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 7. a(n) = L(n+2) for n >=1, where L = A000032 (Lucas numbers). G.f.: (-2 - 2 x - x^2)/(-1 + x + x^2). MATHEMATICA Join[{2}, LinearRecurrence[{1, 1}, {4, 7}, 40]] CROSSREFS Cf. A288216, A163695, A080023, A000204. Sequence in context: A289131 A054352 A091838 * A004696 A293418 A289077 Adjacent sequences:  A288216 A288217 A288218 * A288220 A288221 A288222 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 19 2017 STATUS approved

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Last modified May 8 15:54 EDT 2021. Contains 343666 sequences. (Running on oeis4.)