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 A154377 #43 Sep 27 2022 10:21:52
%S A154377 27,104,231,408,635,912,1239,1616,2043,2520,3047,3624,4251,4928,5655,
%T A154377 6432,7259,8136,9063,10040,11067,12144,13271,14448,15675,16952,18279,
%U A154377 19656,21083,22560,24087,25664,27291,28968,30695,32472,34299,36176
%N A154377 a(n) = 25*n^2 + 2*n.
%C A154377 The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as A154375(n)^2 - a(n)*A154379(n)^2 = 1 (see also the second comment in A154375). - _Vincenzo Librandi_, Jan 30 2012
%C A154377 The continued fraction expansion of sqrt(4*a(n)) is [10n; {2, 1, 1, 5n-1, 1, 1, 2, 20n}]. - _Magus K. Chu_, Sep 27 2022
%H A154377 Vincenzo Librandi, <a href="/A154377/b154377.txt">Table of n, a(n) for n = 1..10000</a>
%H A154377 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A154377 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F A154377 G.f.: x*(27 + 23*x)/(1-x)^3.
%F A154377 E.g.f.: (25*x^2 + 27*x)*exp(x). - _G. C. Greubel_, Sep 15 2016
%t A154377 LinearRecurrence[{3,-3,1},{27,104,231},50]
%o A154377 (PARI) a(n)=25*n^2+2*n \\ _Charles R Greathouse IV_, Dec 23 2011
%Y A154377 Cf. A154375, A154379.
%K A154377 nonn,easy
%O A154377 1,1
%A A154377 _Vincenzo Librandi_, Jan 08 2009