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A167373 Expansion of (1+x)*(3*x+1)/(1+x+x^2). 1

%I

%S 1,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,

%T -1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,

%U -2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1,-2,3,-1

%N Expansion of (1+x)*(3*x+1)/(1+x+x^2).

%C Bisection of A138034.

%C Also row 2n of A137276 or A135929.

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, Chapter 22.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1).

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

%F a(n) = a(n-3), n>4.

%F a(n) = - a(n-1) - a(n-2) for n>2.

%F a(n) = 4*sin(2*n*Pi/3)/sqrt(3)-2*cos(2*n*Pi/3) for n>0 with a(0)=1. - _Wesley Ivan Hurt_, Jun 12 2016

%t CoefficientList[Series[(1 + x)*(3*x + 1)/(1 + x + x^2), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 12 2016 *)

%Y Cf. A135929, A138034, A137276.

%K sign,easy

%O 0,2

%A _Jamel Ghanouchi_, Nov 02 2009

%E Edited by _R. J. Mathar_, Nov 03 2009

%E Further edited and extended by _Simon Plouffe_, Nov 23 2009

%E Recomputed by _N. J. A. Sloane_, Dec 20 2009

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)