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 A075841 #41 Jul 14 2025 15:19:55
%S A075841 3,15,87,507,2955,17223,100383,585075,3410067,19875327,115841895,
%T A075841 675176043,3935214363,22936110135,133681446447,779152568547,
%U A075841 4541233964835,26468251220463,154268273357943,899141388927195
%N A075841 Numbers k such that 2*k^2 - 9 is a square.
%C A075841 Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*sqrt(2).
%C A075841 Positive values of x (or y) satisfying x^2 - 6*x*y + y^2 + 36 = 0. - _Colin Barker_, Feb 08 2014
%C A075841 For each member t of the sequence there exists a nonnegative r such that t^2 = r^2 + (r+3)^2. The r values are in A241976. Example: 87^2 = 60^2 + 63^2. - _Bruno Berselli_, Jul 10 2017
%D A075841 A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966.
%D A075841 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, pp. 341-400.
%D A075841 Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, pp. 139-147.
%H A075841 Vincenzo Librandi, <a href="/A075841/b075841.txt">Table of n, a(n) for n = 1..200</a>
%H A075841 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A075841 J. J. O'Connor and E. F. Robertson, <a href="https://mathshistory.st-andrews.ac.uk/HistTopics/Pell/">Pell's Equation</a>
%H A075841 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellEquation.html">Pell Equation.</a>
%H A075841 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F A075841 a(n) = 3*sqrt(2)/4*((1+sqrt(2))^(2*n-1)-(1-sqrt(2))^(2*n-1)) = 6*a(n-1) - a(n-2).
%F A075841 G.f.: 3*x*(1-x)/(1-6*x+x^2). - _Philippe Deléham_, Nov 17 2008
%F A075841 a(n) = 3*A001653(n). - _R. J. Mathar_, Sep 27 2014
%t A075841 CoefficientList[Series[3 (1 - x)/(1 - 6 x + x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 11 2014 *)
%t A075841 LinearRecurrence[{6,-1},{3,15},20] (* _Harvey P. Dale_, Jun 05 2023 *)
%o A075841 (PARI) isok(n) = issquare(2*n^2-9); \\ _Michel Marcus_, Jul 10 2017
%K A075841 nonn,easy
%O A075841 1,1
%A A075841 _Gregory V. Richardson_, Oct 14 2002