A288317 a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12.

2, 4, 7, 12, 22, 40, 75, 139, 262, 489, 922, 1726, 3252, 6097, 11479, 21540, 40531, 76096, 143130, 268816, 505483, 949575, 1785262, 3354205, 6305358, 11847874, 22270276, 41848977, 78658699, 147817204, 277825071, 522110308, 981292414, 1844155992, 3465987547

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->0001, 1->00, starting with 00; see A288314.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -1).

Formula

a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12.

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

Mathematica

Join[{2}, LinearRecurrence[{1, 3, -2, -1}, {4, 7, 12, 22}, 40]]

Crossrefs

Cf. A288314.

Sequence in context: A289019 A254685 A002573 * A064492 A000072 A268306

Adjacent sequences: A288314 A288315 A288316 * A288318 A288319 A288320

Keyword

nonn,easy

Author

Clark Kimberling, Jun 09 2017

Status

approved