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%I #28 Sep 08 2022 08:45:29
%S 9,21,57,129,249,429,681,1017,1449,1989,2649,3441,4377,5469,6729,8169,
%T 9801,11637,13689,15969,18489,21261,24297,27609,31209,35109,39321,
%U 43857,48729,53949,59529,65481,71817,78549,85689,93249,101241,109677,118569
%N a(n) = 2*n^3 - 2*n + 9.
%C All numbers generated by the irreducible polynomial 2*n^3-2*n+9 are composite (indeed, they are multiples of 3). Largest prime factor A127990, smallest prime factor A127991, number of prime factors A127992.
%H Vincenzo Librandi, <a href="/A127989/b127989.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 2*(n-1)*n*(n+1)+9 = 3*(2*A007290(n+1)+3).
%F G.f.: 3*x*(3-5*x+9*x^2-3*x^3)/(1-x)^4. - _Bruno Berselli_, Sep 09 2011
%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Wesley Ivan Hurt_, Oct 11 2021
%t Table[2x^3 - 2x + 9, {x, 1, 100}]
%t LinearRecurrence[{4,-6,4,-1}, {9, 21, 57, 129}, 50] (* _G. C. Greubel_, May 08 2018 *)
%o (Magma) [2*(n-1)*n*(n+1)+9: n in [1..50]]; // _Vincenzo Librandi_, Sep 13 2011
%o (PARI) a(n)=2*n^3-2*n+9 \\ _Charles R Greathouse IV_, Sep 30 2015
%Y Cf. A127990, A127991, A127992. Subsequence of A017629.
%K nonn,easy
%O 1,1
%A _Artur Jasinski_, Feb 10 2007
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