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%I #22 Apr 05 2023 13:49:09
%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
%p A167373 := proc(n)
%p option remember;
%p if n < 4 then
%p op(n+1,[1,3,-1,-2]) ;
%p else
%p procname(n-3) ;
%p end if;
%p end proc:
%p seq(A167373(n),n=0..20) ; # _R. J. Mathar_, Feb 06 2020
%t CoefficientList[Series[(1 + x)*(3*x + 1)/(1 + x + x^2), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 12 2016 *)
%t LinearRecurrence[{-1,-1},{1,3,-1},120] (* _Harvey P. Dale_, Apr 05 2023 *)
%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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