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%I #26 Sep 08 2022 08:45:48
%S 1083,8124,26703,62400,120795,207468,327999,487968,692955,948540,
%T 1260303,1633824,2074683,2588460,3180735,3857088,4623099,5484348,
%U 6446415,7514880,8695323,9993324,11414463,12964320,14648475,16472508
%N a(n) = 3*n*(310*n^2 + 63*n - 12).
%C Old name was: Related to A165808; this sequence is that of rational integer coefficients of sqrt(-1) in the quotients f(x+k*f(x))/f(x) where f(x) = x^3 + 2x +11 and x = 2 +3i.
%H G. C. Greubel, <a href="/A165809/b165809.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F From _R. J. Mathar_, Sep 30 2009: (Start)
%F G.f.: 3*x*(361 + 1264*x + 235*x^2)/(1-x)^4.
%F a(n) = 3*n*(310*n^2 + 63*n - 12). (End)
%F From _G. C. Greubel_, Apr 09 2016: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F E.g.f.: 3*x*(361 + 993*x + 310*x^2)*exp(x). (End)
%p seq(3*n*(310*n^2 + 63*n - 12), n=1..35); # _G. C. Greubel_, Sep 02 2019
%t LinearRecurrence[{4, -6, 4, -1}, {1083, 8124, 26703, 62400}, 50] (* _G. C. Greubel_, Apr 09 2016 *)
%t Table[3n(310n^2+63n-12),{n,30}] (* _Harvey P. Dale_, Jun 15 2021 *)
%o (PARI) a(n)=3*n*(310*n^2+63*n-12) \\ _Charles R Greathouse IV_, Jul 07 2013
%o (Magma) [3*n*(310*n^2 + 63*n - 12): n in [1..35]]; // _G. C. Greubel_, Sep 02 2019
%o (Sage) [3*n*(310*n^2 + 63*n - 12) for n in (1..35)] # _G. C. Greubel_, Sep 02 2019
%o (GAP) List([1..35], n-> 3*n*(310*n^2 + 63*n - 12)); # _G. C. Greubel_, Sep 02 2019
%K nonn,easy
%O 1,1
%A _A.K. Devaraj_, Sep 29 2009
%E More terms from _R. J. Mathar_, Sep 30 2009
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