A287381 a(n) = a(n-1) + 2*a(n-2) - a(n-3), where a(0) = 2, a(1) = 4, a(2) = 7.

2, 4, 7, 13, 23, 42, 75, 136, 244, 441, 793, 1431, 2576, 4645, 8366, 15080, 27167, 48961, 88215, 158970, 286439, 516164, 930072, 1675961, 3019941, 5441791, 9805712, 17669353, 31838986, 57371980, 103380599, 186285573, 335674791, 604865338, 1089929347

Offset: 0

Author

Clark Kimberling, Jun 07 2017

Keywords

• nonn
• easy

Comments

Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0010, 1->10, starting with 00; see A287931.

Links

• Clark Kimberling, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (1, 2, -1).

Crossrefs

Cf. A287931, A078038 (signed version).

Programs

Mathematica

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

Formula

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

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