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 A324266 #10 Sep 08 2022 08:46:24 %S A324266 2,98,4802,235298,11529602,564950498,27682574402,1356446145698, %T A324266 66465861139202,3256827195820898,159584532595224002, %U A324266 7819642097165976098,383162462761132828802,18774960675295508611298,919973073089479921953602,45078680581384516175726498,2208855348487841292610598402 %N A324266 a(n) = 2*49^n. %C A324266 x = A324265(n) and y = a(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma). %H A324266 K. Chakraborty, A. Hoque, R. Sharma, <a href="https://arxiv.org/abs/1812.11874">Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations</a>, arXiv:1812.11874 [math.NT], 2018. %F A324266 O.g.f.: 2/(1 - 49*x). %F A324266 E.g.f.: 2*exp(49*x). %F A324266 a(n) = 49*a(n-1) for n > 0. %F A324266 a(n) = (49/2)*(A109808(n))^2. %e A324266 For A324265(0) = 5 and a(0) = 2, 5^2 + 7 = 32 = 4*2^3. %p A324266 a:=n->2*49^n: seq(a(n), n=0..20); %t A324266 2*49^Range[0,20] %o A324266 (GAP) List([0..20], n->2*49^n); %o A324266 (Magma) [2*49^n: n in [0..20]]; %o A324266 (PARI) a(n) = 2*49^n; %Y A324266 Cf. A324265 (5*343^n), A000290 (n^2), A000578 (n^3), A109808 (2*7^(n-1)). %K A324266 nonn,easy %O A324266 0,1 %A A324266 _Stefano Spezia_, Feb 20 2019