A287525 a(n) = a(n-1) + a(n-2) - a(n-3) +a(n-4) + a(n-5) for n >= 6, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 19, a(5) = 31.

2, 4, 7, 12, 19, 31, 49, 80, 129, 210, 339, 549, 887, 1436, 2323, 3760, 6083, 9843, 15925, 25768, 41693, 67462, 109155, 176617, 285771, 462388, 748159, 1210548, 1958707, 3169255, 5127961, 8297216, 13425177, 21722394, 35147571, 56869965, 92017535, 148887500

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->1000, 10->001, starting with 00; see A287372.

Links

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

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

Formula

a(n) = a(n-1) + a(n-2) - a(n-3) +a(n-4) + a(n-5) for n >= 6, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 19, a(5) = 31.

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

Mathematica

Join[{2}, LinearRecurrence[{1, 1, -1, 1, 1}, {4, 7, 12, 19, 31}, 40]]

Crossrefs

Cf. A287372.

Sequence in context: A343661 A342229 A326080 * A244472 A279890 A018147

Adjacent sequences: A287522 A287523 A287524 * A287526 A287527 A287528

Keyword

nonn,easy

Author

Clark Kimberling, Jun 18 2017

Status

approved