A288380 a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5) for n >= 1, where a(0) = 2, a(1) = 4, a(2) = 7. a(3) = 11, a(4) = 20.

2, 4, 7, 11, 20, 38, 70, 130, 245, 461, 866, 1630, 3070, 5780, 10883, 20495, 38596, 72682, 136874, 257762, 485417, 914137, 1721506, 3241946, 6105242, 11497412, 21651967, 40775059, 76787732, 144606926, 272324270, 512842018, 965785885, 1818771365, 3425116610

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->10, starting with 00; see A288377.

Links

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

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

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5) for n >= 1, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 20.

G.f.: (-2 + 2 x - x^2 + 4 x^3 - 2 x^4)/(-1 + 3 x - 3 x^2 + 3 x^3 - 3 x^4 + x^5).

Mathematica

LinearRecurrence[{3, -3, 3, -3, 1}, {2, 4, 7, 11, 20}, 40]

Crossrefs

Cf. A288377.

Sequence in context: A024501 A160393 A018173 * A369581 A146156 A304916

Adjacent sequences: A288377 A288378 A288379 * A288381 A288382 A288383

Keyword

nonn,easy

Author

Clark Kimberling, Jun 10 2017

Status

approved