A286350 - OEIS

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

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OFFSET

0,2

COMMENTS

This is b(n) inA286311(n). As mentioned inA286311,the pairA286311(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 fromColin Barker,May 09 2017

STATUS

approved