A286350 a(n) = 2*a(n-1) - a(n-2) + a(n-4) for n>3, a(0)=0, a(1)=a(2)=2, a(3)=3.

0, 2, 2, 3, 4, 7, 12, 20, 32, 51, 82, 133, 216, 350, 566, 915, 1480, 2395, 3876, 6272, 10148, 16419, 26566, 42985, 69552, 112538, 182090, 294627, 476716, 771343, 1248060, 2019404, 3267464, 5286867, 8554330, 13841197, 22395528, 36236726, 58632254, 94868979

Offset: 0

Author

Paul Curtz, May 08 2017

Keywords

• nonn
• easy

Comments

This is b(n) in A286311(n). As mentioned in A286311, the pair A286311(n) and, here a(n), are autosequences of the first kind.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1).

Crossrefs

Cf. A022086, A128834, A226956 (same recurrence), A286311.

Programs

Magma

I:=[0,2,2,3]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2) + Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 15 2018

Mathematica

LinearRecurrence[{2, -1, 0, 1}, {0, 2, 2, 3}, 40] (* or *)
CoefficientList[Series[x (2 - 2 x + x^2)/((1 - x + x^2) (1 - x - x^2)), {x, 0, 39}], x] (* Michael De Vlieger, May 09 2017 *)

PARI

concat(0, Vec(x*(2 - 2*x + x^2) / ((1 - x + x^2)*(1 - x - x^2)) + O(x^60))) \\ Colin Barker, May 09 2017

Formula

a(n) = A286311(n) + A128834(n).

a(n) = A022086(n) - A286311(n).

a(n) = (A022086(n) + A128834(n))/2.

G.f.: x*(2 - 2*x + x^2) / ((1 - x + x^2)*(1 - x - x^2)). - Colin Barker, May 09 2017

Extensions

More terms from Colin Barker, May 09 2017