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%I #26 Feb 20 2023 03:13:36
%S 21,221,621,1221,2021,3021,4221,5621,7221,9021,11021,13221,15621,
%T 18221,21021,24021,27221,30621,34221,38021,42021,46221,50621,55221,
%U 60021,65021,70221,75621,81221,87021,93021,99221,105621,112221,119021,126021,133221,140621,148221
%N a(n) = 100*n^2 + 100*n + 21.
%H Vincenzo Librandi, <a href="/A152161/b152161.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A017305(n)*A017353(n) = A061037(10*n+3).
%F From _Amiram Eldar_, Feb 20 2023: (Start)
%F Sum_{n>=0} 1/a(n) = sqrt(5-2*sqrt(5))*Pi/40.
%F Sum_{n>=0} (-1)^n/a(n) = (sqrt(10-2*sqrt(5))*log(cot(Pi/20)) + sqrt(10+2*sqrt(5))*log(tan(3*Pi/20)))/40.
%F Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/10)/phi, where phi is the golden ratio (A001622).
%F Product_{n>=0} (1 + 1/a(n)) = 2*cos(sqrt(3)*Pi/10)/phi. (End)
%t Table[100*n^2 + 100*n + 21, {n,0,50}] (* _G. C. Greubel_, Sep 20 2018 *)
%t LinearRecurrence[{3,-3,1},{21,221,621},40] (* _Harvey P. Dale_, Dec 06 2018 *)
%o (Magma) [(10*n+3)*(10*n+7): n in [0..40]]; // _Vincenzo Librandi_, Jul 28 2011
%o (PARI) a(n)=100*n*(n+1)+21 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y Cf. A001622, A017305, A017353, A061037.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Nov 27 2008
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