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 A156677 #31 Oct 19 2024 13:01:30
%S A156677 43,6,131,418,867,1478,2251,3186,4283,5542,6963,8546,10291,12198,
%T A156677 14267,16498,18891,21446,24163,27042,30083,33286,36651,40178,43867,
%U A156677 47718,51731,55906,60243,64742,69403,74226,79211,84358,89667,95138,100771,106566,112523,118642
%N A156677 a(n) = 81*n^2 - 118*n + 43.
%C A156677 The identity (6561*n^2 - 9558*n + 3482)^2 - (81*n^2 - 118*n + 43)*(729*n - 531)^2 = 1 can be written as A156773(n)^2 - a(n)*A156771(n)^2 = 1 for n > 0.
%C A156677 For n >= 1, the continued fraction expansion of sqrt(a(n)) is [9n-7; {2, 4, 9n-7, 4, 2, 18n-14}]. For n=1, this collapses to [2; {2, 4}]. - _Magus K. Chu_, Sep 09 2022
%H A156677 Vincenzo Librandi, <a href="/A156677/b156677.txt">Table of n, a(n) for n = 0..10000</a>
%H A156677 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A156677 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A156677 G.f.: (-43+123*x-242*x^2)/(x-1)^3.
%F A156677 For n > 1: a(n) = A171198(n-2) - A017305(n-2). - _Reinhard Zumkeller_, Jul 13 2010
%F A156677 E.g.f.: exp(x)*(43 - 37*x + 81*x^2). - _Elmo R. Oliveira_, Oct 19 2024
%t A156677 LinearRecurrence[{3,-3,1},{43,6,131},40]
%o A156677 (Magma) I:=[43, 6, 131]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o A156677 (PARI) a(n)=81*n^2-118*n+43 \\ _Charles R Greathouse IV_, Dec 23 2011
%Y A156677 Cf. A017305, A156771, A156773, A171198.
%K A156677 nonn,easy
%O A156677 0,1
%A A156677 _Vincenzo Librandi_, Feb 15 2009
%E A156677 Edited by _Charles R Greathouse IV_, Jul 25 2010