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

%I A167373 #22 Apr 05 2023 13:49:09
%S A167373 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 A167373 -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 A167373 -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 A167373 Expansion of (1+x)*(3*x+1)/(1+x+x^2).
%C A167373 Bisection of A138034.
%C A167373 Also row 2n of A137276 or A135929.
%D A167373 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 A167373 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1).
%F A167373 G.f.: (1+x)*(3*x+1)/(1+x+x^2).
%F A167373 a(n) = a(n-3), n>4.
%F A167373 a(n) = - a(n-1) - a(n-2) for n>2.
%F A167373 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 A167373 := proc(n)
%p A167373     option remember;
%p A167373     if n < 4 then
%p A167373         op(n+1,[1,3,-1,-2]) ;
%p A167373     else
%p A167373         procname(n-3) ;
%p A167373     end if;
%p A167373 end proc:
%p A167373 seq(A167373(n),n=0..20) ; # _R. J. Mathar_, Feb 06 2020
%t A167373 CoefficientList[Series[(1 + x)*(3*x + 1)/(1 + x + x^2), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 12 2016 *)
%t A167373 LinearRecurrence[{-1,-1},{1,3,-1},120] (* _Harvey P. Dale_, Apr 05 2023 *)
%Y A167373 Cf. A135929, A138034, A137276.
%K A167373 sign,easy
%O A167373 0,2
%A A167373 _Jamel Ghanouchi_, Nov 02 2009
%E A167373 Edited by _R. J. Mathar_, Nov 03 2009
%E A167373 Further edited and extended by _Simon Plouffe_, Nov 23 2009
%E A167373 Recomputed by _N. J. A. Sloane_, Dec 20 2009