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%I #21 Jun 18 2021 07:24:54
%S 0,-1,4,-13,40,-121,364,-1093,3280,-9841,29524,-88573,265720,-797161,
%T 2391484,-7174453,21523360,-64570081,193710244,-581130733,1743392200,
%U -5230176601,15690529804,-47071589413,141214768240,-423644304721,1270932914164
%N a(n) = (-1)^n * (3^n - 1)/2.
%H G. C. Greubel, <a href="/A076040/b076040.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-3).
%F Equals A038608 o A003462 = A033999 * A003462, i.e., a(n) = (-1)^n*A003462(n) = (-1)^A003462(n)*A003462(n) = A038608(A003462(n)). - _M. F. Hasler_, Oct 21 2014
%F From _Colin Barker_, Oct 22 2014: (Start)
%F a(n) = -4*a(n-1) - 3*a(n-2).
%F G.f.: -x / ((1+x)*(1+3*x)). (End)
%F E.g.f.: (-1)*exp(-2*x)*sinh(x). - _G. C. Greubel_, Jun 18 2021
%t Table[(-1)^n*(3^n -1)/2, {n, 0, 30}] (* _G. C. Greubel_, Jun 18 2021 *)
%o (PARI) concat(0, Vec(-x/((x+1)*(3*x+1)) + O(x^100))) \\ _Colin Barker_, Oct 22 2014
%o (Sage) [(-1)^n*(3^n -1)/2 for n in (0..30)] # _G. C. Greubel_, Jun 18 2021
%Y Cf. A003462, A033999.
%K sign,easy
%O 0,3
%A _M. F. Hasler_, Oct 21 2014
%E Former duplicate of A003462 changed to the signed variant by _M. F. Hasler_, Oct 21 2014
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