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%I #18 Sep 08 2022 08:46:21
%S 37,999,26973,728271,19663317,530909559,14334558093,387033068511,
%T 10449892849797,282147106944519,7617971887502013,205685240962554351,
%U 5553501505988967477,149944540661702121879,4048502597865957290733,109309570142380846849791,2951358393844282864944357
%N a(n) = 37*27^n.
%C x = a(n) and y = A002042(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 3^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).
%H 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.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (27).
%F O.g.f.: 37/(1 - 27*x).
%F E.g.f.: 37*exp(27*x).
%F a(n) = 27*a(n-1) for n > 0.
%F a(n) = 37*A009971(n).
%e For a(0) = 37 and A002042(0) = 7, 37^2 + 3 = 1372 = 4*7^3.
%p a:=n->37*27^n: seq(a(n), n=0..20);
%t 37*27^Range[0,20]
%o (GAP) List([0..20], n->37*27^n);
%o (Magma) [37*27^n: n in [0..20]];
%o (PARI) a(n) = 37*27^n;
%Y Cf. A002042 (7*4^n), A009971 (27^n), A000290 (n^2), A000578 (n^3).
%K nonn,easy
%O 0,1
%A _Stefano Spezia_, Feb 18 2019
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