A289077 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.

2, 4, 7, 11, 18, 30, 47, 74, 114, 176, 269, 411, 625, 950, 1441, 2185, 3310, 5013, 7589, 11487, 17384, 26306, 39804, 60225, 91120, 137860, 208573, 315552, 477400, 722254, 1092691, 1653113, 2500967, 3783660, 5724223, 8660047, 13101596, 19821099, 29986891

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

Cf. A289074.

Sequence in context: A288219 A004696 A293418 * A228560 A018063 A289004

Adjacent sequences: A289074 A289075 A289076 * A289078 A289079 A289080

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved