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 A177059 #34 Nov 30 2024 12:37:14
%S A177059 6,56,156,306,506,756,1056,1406,1806,2256,2756,3306,3906,4556,5256,
%T A177059 6006,6806,7656,8556,9506,10506,11556,12656,13806,15006,16256,17556,
%U A177059 18906,20306,21756,23256,24806,26406,28056,29756,31506,33306,35156,37056,39006,41006,43056
%N A177059 a(n) = 25*n^2 + 25*n + 6.
%H A177059 Vincenzo Librandi, <a href="/A177059/b177059.txt">Table of n, a(n) for n = 0..10000</a>
%H A177059 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A177059 a(n) = (5*n + 2)*(5*n + 3).
%F A177059 a(n) = 50*n + a(n-1) with a(0)=6.
%F A177059 a(n) = 25*A002061(n+1) - 19. - _Reinhard Zumkeller_, Jun 16 2010
%F A177059 G.f.: (6 + 38*x + 6*x^2)/(1-x)^3. - _Vincenzo Librandi_, Feb 03 2012
%F A177059 From _Amiram Eldar_, Jan 23 2022: (Start)
%F A177059 Sum_{n>=0} 1/a(n) = sqrt(1 - 2/sqrt(5))*Pi/5.
%F A177059 Sum_{n>=0} (-1)^n/a(n) = 2*log(phi)/sqrt(5) - 2*log(2)/5, where phi is the golden ratio (A001622).
%F A177059 Product_{n>=0} (1 - 1/a(n)) = 2*sqrt(2/(5+sqrt(5))) * cos(Pi/(2*sqrt(5))).
%F A177059 Product_{n>=0} (1 + 1/a(n)) = sqrt(2 - 2/sqrt(5)) * cosh(sqrt(3)*Pi/10).
%F A177059 Product_{n>=0} (1 - 2/a(n)) = 1/phi. (End)
%F A177059 From _Elmo R. Oliveira_, Oct 24 2024: (Start)
%F A177059 E.g.f.: exp(x)*(6 + 25*x*(2 + x)).
%F A177059 a(n) = A016873(n)*A016885(n) = 2*A061793(n).
%F A177059 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A177059 LinearRecurrence[{3, -3, 1}, {6, 56, 156}, 50] (* _Vincenzo Librandi_, Feb 03 2012 *)
%t A177059 Table[25n^2+25n+6,{n,0,40}] (* _Harvey P. Dale_, Mar 30 2019 *)
%o A177059 (PARI) a(n)=25*n^2+25*n+6 \\ _Charles R Greathouse IV_, Dec 28 2011
%o A177059 (Magma) I:=[6, 56, 156]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 03 2012
%Y A177059 Cf. A001545, A001622, A002061, A177060, A177065, A177071, A177072, A177073.
%Y A177059 Cf. A016873, A016885, A061793.
%K A177059 nonn,easy
%O A177059 0,1
%A A177059 _Vincenzo Librandi_, May 31 2010