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%I #29 Sep 08 2022 08:45:29
%S 1,-2,1,3,-7,4,10,-25,16,33,-89,63,108,-316,245,350,-1119,943,1121,
%T -3952,3598,3539,-13920,13625,10971,-48897,51256,33208,-171287,191694,
%U 97265,-598325,713161,271388,-2083934
%N Expansion of 1/(1 + 2*x + 3*x^2 + x^3).
%C Row sums of A127895. Series reversion is A127897.
%H G. C. Greubel, <a href="/A127896/b127896.txt">Table of n, a(n) for n = 0..1000</a>
%H Paul Barry, <a href="https://arxiv.org/abs/2104.01644">Centered polygon numbers, heptagons and nonagons, and the Robbins numbers</a>, arXiv:2104.01644 [math.CO], 2021.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-3,-1).
%F a(n) = Sum_{k=0..n} (-1)^(n-k)*C(n+2k+2,n-k).
%F a(n) = -2*a(n-1) -3*a(n-2) -a(n-3), n>=3. - _Vincenzo Librandi_, Mar 22 2011
%t CoefficientList[Series[1/(1+2x+3x^2+x^3),{x,0,40}],x] (* _Harvey P. Dale_, Apr 19 2011 *)
%t LinearRecurrence[{-2, -3, -1}, {1, -2, 1}, 30] (* _G. C. Greubel_, Apr 29 2018 *)
%o (PARI) x='x+O('x^50); Vec(1/(1+2*x+3*x^2+x^3)) \\ _G. C. Greubel_, Apr 29 2018
%o (Magma) I:=[1, -2, 1]; [n le 3 select I[n] else -2*Self(n-1) -3*Self(n-2) -Self(n-3): n in [1..50]]; // _G. C. Greubel_, Apr 29 2018
%Y Cf. A127895, A127897.
%K easy,sign
%O 0,2
%A _Paul Barry_, Feb 04 2007
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