This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A152161 #30 Nov 29 2024 13:50:54
%S A152161 21,221,621,1221,2021,3021,4221,5621,7221,9021,11021,13221,15621,
%T A152161 18221,21021,24021,27221,30621,34221,38021,42021,46221,50621,55221,
%U A152161 60021,65021,70221,75621,81221,87021,93021,99221,105621,112221,119021,126021,133221,140621,148221
%N A152161 a(n) = 100*n^2 + 100*n + 21.
%H A152161 Vincenzo Librandi, <a href="/A152161/b152161.txt">Table of n, a(n) for n = 0..10000</a>
%H A152161 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152161 a(n) = A017305(n)*A017353(n) = A061037(10*n+3).
%F A152161 From _Amiram Eldar_, Feb 20 2023: (Start)
%F A152161 Sum_{n>=0} 1/a(n) = sqrt(5-2*sqrt(5))*Pi/40.
%F A152161 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 A152161 Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/10)/phi, where phi is the golden ratio (A001622).
%F A152161 Product_{n>=0} (1 + 1/a(n)) = 2*cos(sqrt(3)*Pi/10)/phi. (End)
%F A152161 From _Elmo R. Oliveira_, Nov 27 2024: (Start)
%F A152161 G.f.: (21 + 158*x + 21*x^2)/(1-x)^3.
%F A152161 E.g.f.: (21 + 200*x + 100*x^2)*exp(x).
%F A152161 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
%t A152161 Table[100*n^2 + 100*n + 21, {n,0,50}] (* _G. C. Greubel_, Sep 20 2018 *)
%t A152161 LinearRecurrence[{3,-3,1},{21,221,621},40] (* _Harvey P. Dale_, Dec 06 2018 *)
%o A152161 (Magma) [(10*n+3)*(10*n+7): n in [0..40]]; // _Vincenzo Librandi_, Jul 28 2011
%o A152161 (PARI) a(n)=100*n*(n+1)+21 \\ _Charles R Greathouse IV_, Jul 28 2011
%Y A152161 Cf. A001622, A017305, A017353, A061037.
%K A152161 nonn,easy
%O A152161 0,1
%A A152161 _Paul Curtz_, Nov 27 2008