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 A075836 #30 Jul 14 2025 15:19:55
%S A075836 0,2,4,18,80,154,684,3038,5848,25974,115364,222070,986328,4380794,
%T A075836 8432812,37454490,166354808,320224786,1422284292,6317101910,
%U A075836 12160109056,54009348606,239883517772,461763919342,2050932962736
%N A075836 Numbers k such that 10*k^2 + 9 is a square.
%C A075836 (5/4)*a(n)^2 +1 is a triangular number. - _Bruno Berselli_, Aug 17 2013
%D A075836 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 A075836 L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, pp. 341-400.
%D A075836 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 A075836 Vincenzo Librandi, <a href="/A075836/b075836.txt">Table of n, a(n) for n = 1..1000</a>
%H A075836 J. J. O'Connor and E. F. Robertson, <a href="https://mathshistory.st-andrews.ac.uk/HistTopics/Pell/">Pell's Equation</a>
%H A075836 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellEquation.html">Pell Equation.</a>
%H A075836 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,38,0,0,-1).
%F A075836 From _Gregory V. Richardson_, Oct 16 2002: (Start)
%F A075836 Limit_{n->oo} a(n)/a(n-3) = 19 + 6*sqrt(10).
%F A075836 Limit_{n->oo} a(3*n)/a(3*n-1) = (11 + 2*sqrt(10))/9.
%F A075836 Limit_{n->oo} a(3*n+1)/a(3*n) = (7 + 2*sqrt(10))/3.
%F A075836 Limit_{n->oo} a(3*n+2)/a(3*n+1) = (7 + 2*sqrt(10))/3. (End)
%F A075836 G.f.: 2*x^2*(1+2*x+9*x^2+2*x^3+x^4) / ( 1-38*x^3+x^6 ). - _R. J. Mathar_, Jul 03 2011
%F A075836 a(n) = 2*A075873(n). - _R. J. Mathar_, Jul 03 2011
%t A075836 CoefficientList[Series[2 x (1 + 2 x + 9 x^2 + 2 x^3 + x^4) / (1 - 38 x^3 + x^6), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)
%o A075836 (Magma) I:=[0,2,4,18,80,154]; [n le 6 select I[n] else 38*Self(n-3)-Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Aug 17 2013
%Y A075836 Cf. A221874.
%K A075836 nonn,easy
%O A075836 1,2
%A A075836 _Gregory V. Richardson_, Oct 14 2002