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

0,2

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).

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A173433 A053638 A051920 * A023105 A281723 A011784

Adjacent sequences: A286347 A286348 A286349 * A286351 A286352 A286353

Keyword

nonn,easy

Author

Paul Curtz, May 08 2017

Extensions

More terms from Colin Barker, May 09 2017

Status

approved