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%I #75 Feb 19 2023 03:34:17
%S 2,20,56,110,182,272,380,506,650,812,992,1190,1406,1640,1892,2162,
%T 2450,2756,3080,3422,3782,4160,4556,4970,5402,5852,6320,6806,7310,
%U 7832,8372,8930,9506,10100,10712,11342,11990,12656,13340,14042,14762,15500,16256,17030
%N a(n) = (3*n+1)*(3*n+2).
%C The oblong numbers (A002378) not divisible by 3. - _Gionata Neri_, May 10 2015
%H T. D. Noe, <a href="/A001504/b001504.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A060544(n+1)*2.
%F Sum_{k>=0} 1/a(k) = (Pi/3)/sqrt(3) = A073010. - _Benoit Cloitre_, Aug 20 2002
%F a(n) = 18*n + a(n-1) with a(0) = 2. - _Vincenzo Librandi_, Nov 12 2010
%F Sum_{n>=0} (-1)^n/a(n) = 2*log(2)/3. - _Amiram Eldar_, Jan 14 2021
%F G.f.: -2*(x^2+7*x+1)/(x-1)^3. - _Alois P. Heinz_, Feb 28 2021
%F From _Amiram Eldar_, Feb 19 2023: (Start)
%F a(n) = A016777(n)*A016789(n).
%F Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/6)/sqrt(3).
%F Product_{n>=0} (1 + 1/a(n)) = 2*cosh(sqrt(3)*Pi/6)/sqrt(3). (End)
%p A001504:=n->(3*n+1)*(3*n+2): seq(A001504(n), n=0..100); # _Wesley Ivan Hurt_, Jan 29 2017
%t Table[(3*n+1)*(3*n+2),{n,50}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2012 *)
%o (PARI) a(n)=(3*n+1)*(3*n+2) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Subsequence of A002378.
%Y Cf. A016777, A016789, A060544, A073010.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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