A289004 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) - a(n-5) + a(n-7) - a(n-8) - a(n-10) for n >= 10, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 31, a(6) = 52, a(7) = 89, a(9) = 151, a(9) = 257.

2, 4, 7, 11, 18, 31, 52, 89, 151, 257, 438, 748, 1277, 2179, 3719, 6348, 10837, 18499, 31579, 53908, 92027, 157099, 268182, 457812, 781531, 1334153, 2277532, 3887973, 6637157, 11330291, 19341939, 33018621, 56366084, 96222539, 164261491, 280410777, 478689212

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->001, 10->010, starting with 00; see A289001.

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2,-1,0,1,-1,0,-1).

Formula

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) - a(n-5) + a(n-7) - a(n-8) - a(n-10) for n >= 10, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 31, a(6) = 52, a(7) = 89, a(9) = 151, a(9) = 257.

G.f.: (2 + x^2 + x^3 - x^4 - 2*x^6 - x^7 - 2*x^8 - 3*x^9) / ((1 - x)*(1 - x - 2*x^4 - x^5 - x^6 - 2*x^7 - x^8 - x^9)). - Colin Barker, Jun 26 2017

Mathematica

LinearRecurrence[{2, -1, 0, 2, -1, 0, 1, -1, 0, -1}, {2, 4, 7, 11, 18, 31, 52, 89, 151, 257}, 20]

Prog

(PARI) Vec((2 + x^2 + x^3 - x^4 - 2*x^6 - x^7 - 2*x^8 - 3*x^9) / ((1 - x)*(1 - x - 2*x^4 - x^5 - x^6 - 2*x^7 - x^8 - x^9)) + O(x^40)) \\ Colin Barker, Jun 26 2017

Crossrefs

Cf. A288216.

Sequence in context: A289077 A228560 A018063 * A000570 A239552 A023426

Adjacent sequences: A289001 A289002 A289003 * A289005 A289006 A289007

Keyword

nonn,easy

Author

Clark Kimberling, Jun 26 2017

Status

approved