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%I #18 Oct 21 2022 21:14:20
%S 3,29,114,310,685,1323,2324,3804,5895,8745,12518,17394,23569,31255,
%T 40680,52088,65739,81909,100890,122990,148533,177859,211324,249300,
%U 292175,340353,394254,454314,520985,594735,676048,765424,863379,970445,1087170
%N [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 4}.
%H Vincenzo Librandi, <a href="/A024386/b024386.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = n(n+1)(4n^2+8n-3)/6.
%F G.f.: x*(-3-14*x+x^2) / (x-1)^5 . - _R. J. Mathar_, Oct 08 2011
%t Table[n (n + 1) (4 n^2 + 8 n - 3) / 6, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {3, 29, 114, 310, 685}, 60] (* _Vincenzo Librandi_, Aug 12 2018 *)
%o (Magma)[n*(n+1)*(4*n^2+8*n-3)/6: n in [1..60]]; // _Vincenzo Librandi_, Aug 12 2018
%o (PARI) a(n)=n*(n+1)*(4*n^2+8*n-3)/6 \\ _Charles R Greathouse IV_, Oct 21 2022
%K nonn,easy
%O 1,1
%A _Clark Kimberling_
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