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%I #11 Sep 08 2022 08:44:49
%S 1,1,4,6,10,18,29,47,78,126,204,332,537,869,1408,2278,3686,5966,9653,
%T 15619,25274,40894,66168,107064,173233,280297,453532,733830,1187362,
%U 1921194,3108557,5029751,8138310,13168062,21306372,34474436,55780809,90255245,146036056,236291302,382327358
%N n-th diagonal sum of right justified array T given by A027960.
%H G. C. Greubel, <a href="/A027976/b027976.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-1,-1).
%F G.f.: (1 + 2*x^2)/((1-x^3)*(1-x-x^2)).
%F From _G. C. Greubel_, Sep 26 2019: (Start)
%F a(n) = (Fibonacci(n) + 4*Fibonacci(n+1) - A102283(n) - 2)/2.
%F a(n) = (Fibonacci(n+1) + Lucas(n+2) - 2*sin(2*Pi*n/3)/sqrt(3) - 2)/2. (End)
%p seq(coeff(series((1 + 2*x^2)/((1-x^3)*(1-x-x^2)), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Sep 26 2019
%t LinearRecurrence[{1,1,1,-1,-1}, {1,1,4,6,10}, 41] (* or *) Table[ (Fibonacci[n+1] +LucasL[n+2] -2*Sin[2*Pi*n/3]/Sqrt[3] -2)/2, {n,0,40}] (* _G. C. Greubel_, Sep 26 2019 *)
%o (PARI) my(x='x+O('x^40)); Vec((1 + 2*x^2)/((1-x^3)*(1-x-x^2))) \\ _G. C. Greubel_, Sep 26 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1 + 2*x^2)/((1-x^3)*(1-x-x^2)) )); // _G. C. Greubel_, Sep 26 2019
%o (Sage)
%o def A027976_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1 + 2*x^2)/((1-x^3)*(1-x-x^2))).list()
%o A027976_list(40) # _G. C. Greubel_, Sep 26 2019
%o (GAP) a:=[1,1,4,6,10];; for n in [6..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]-a[n-4]-a[n-5]; od; a; # _G. C. Greubel_, Sep 26 2019
%Y Cf. A000032, A000045, A004695, A027960, A102283.
%K nonn
%O 0,3
%A _Clark Kimberling_
%E Terms a(28) onward added by _G. C. Greubel_, Sep 26 2019
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