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%I #30 Feb 20 2023 03:14:16
%S 11,299,875,1739,2891,4331,6059,8075,10379,12971,15851,19019,22475,
%T 26219,30251,34571,39179,44075,49259,54731,60491,66539,72875,79499,
%U 86411,93611,101099,108875,116939,125291,133931,142859,152075,161579,171371,181451,191819
%N a(n) = (12n+1)*(12n+11).
%H T. D. Noe, <a href="/A001538/b001538.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) = (9 * A001533(n) - 19)/4.
%F a(n) = 288*n + a(n-1) with a(0)=11. - _Vincenzo Librandi_, Nov 12 2010
%F G.f.: -(11 + 266*x + 11*x^2)/(x-1)^3 . - _R. J. Mathar_, Jun 30 2020
%F From _Amiram Eldar_, Feb 20 2023: (Start)
%F a(n) = A017533(n)*A017653(n).
%F Sum_{n>=0} 1/a(n) = (sqrt(3)+2)*Pi/120.
%F Sum_{n>=0} (-1)^n/a(n) = (4*log(sqrt(2)+1) + sqrt(3)*log(5+2*sqrt(6)))/(60*sqrt(2)).
%F Product_{n>=0} (1 - 1/a(n)) = (2*sqrt(2)/(sqrt(3)-1))*cos(sqrt(13/2)*Pi/6).
%F Product_{n>=0} (1 + 1/a(n)) = 2*sqrt(2+sqrt(3))*cos(Pi/sqrt(6)). (End)
%o (PARI) a(n)=(12*n+1)*(12*n+11) \\ _Charles R Greathouse IV_, Jun 16 2017
%Y Cf. A001533, A017533, A017653.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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