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 A383225 #63 May 25 2025 11:05:15
%S A383225 1,11,59,349,2029,11831,68951,401881,2342329,13652099,79570259,
%T A383225 463769461,2703046501,15754509551,91824010799,535189555249,
%U A383225 3119313320689,18180690368891,105964828892651,617608282987021,3599684869029469,20980500931189799,122283320718109319,712719423377466121
%N A383225 a(n) = sqrt(1 + P(n)*P(n+1)*P(n+2)*P(n+3)) where P(n) = A000129(n) are the Pell numbers.
%C A383225 The ratios a(n+1)/a(n) converge to 2*sqrt(2)+3 (A156035).
%H A383225 Seiichi Manyama, <a href="/A383225/b383225.txt">Table of n, a(n) for n = 0..1000</a>
%H A383225 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,5,-1).
%F A383225 a(n) = P(n+1)*P(n+2) - (-1)^n. [Corrected by _Seiichi Manyama_, May 25 2025]
%F A383225 G.f.: (1+6*x-x^2)/((1-6*x+x^2)*(1+x)). - _Joerg Arndt_, Apr 26 2025
%e A383225 a(5) = sqrt(1 + 29*70*169*408) = 11831.
%t A383225 LinearRecurrence[{5, 5, -1}, {1, 11, 59}, 25] (* _Amiram Eldar_, Apr 26 2025 *)
%o A383225 (PARI) Vec((1+6*x-x^2)/((1-6*x+x^2)*(1+x))+O(x^25)) \\ _Joerg Arndt_, Apr 26 2025
%o A383225 (PARI) pell(n) = ([2, 1; 1, 0]^n)[2, 1];
%o A383225 a(n) = pell(n+1)*pell(n+2)-(-1)^n; \\ _Seiichi Manyama_, May 25 2025
%Y A383225 Cf. A000129, A156035.
%K A383225 nonn,easy
%O A383225 0,2
%A A383225 _Jules Beauchamp_, Apr 26 2025