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%I #12 Apr 08 2021 08:22:58
%S 1,12,70,280,905,2568,6666,16220,37580,83780,181074,381488,786715,
%T 1593160,3176210,6246732,12139859,23344760,44471340,84005640,
%U 157483176,293201912,542468100,997906400,1826073525
%N Third convolution of Lucas numbers A000032(n+1), n >= 0.
%H G. C. Greubel, <a href="/A060930/b060930.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-8,5,8,-2,-4,-1).
%F G.f.: ((1+2*x)/(1-x-x^2))^4.
%F a(n) = A060922(n+3, 3) (fourth column of Lucas triangle).
%F a(n) = (2*(25*n^3 + 60*n^2 + 35*n +24)*L(n+2) + (25*n^3 + 90*n^2 + 95*n + 6)*L(n+1))/(3!*5^2), with the Lucas numbers L(n) = A000032(n).
%t Table[((25*n^3+90*n^2+95*n+6)*LucasL[n+4] -12*(5*n^2+10*n-3)*LucasL[n+2])/150, {n, 0, 40}] (* _G. C. Greubel_, Apr 08 2021 *)
%o (Magma)
%o R<x>:=PowerSeriesRing(Integers(), 40);
%o Coefficients(R!( ((1+2*x)/(1-x-x^2))^4 )); // _G. C. Greubel_, Apr 08 2021
%o (Sage)
%o def A060930_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( ((1+2*x)/(1-x-x^2))^4 ).list()
%o A060930_list(40) # _G. C. Greubel_, Apr 08 2021
%Y Cf. A000032, A000204, A004799, A060922, A060929.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Apr 20 2001
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