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%I #17 Sep 08 2022 08:46:24
%S 11,184877,3107227739,52223176609373,877714929273732011,
%T 14751754816303613908877,247932743197614838966495739,
%U 4167005614922312598509893885373,70034863369999307843155786531464011,1177075948659578366919919304234315632877,19783115469121533612823083746266142841763739
%N a(n) = 11*7^(5*n).
%C x = a(n) and y = A324266(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(10*n+1) = 4*y^5 (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 (16807).
%F a(n) = 11*16807^n.
%F O.g.f.: 11/(1 - 16807*x).
%F E.g.f.: 11*exp(16807*x).
%F a(n) = 16807*a(n-1) for n > 0.
%F a(n) = 11*((7/2)*A109808(n))^5.
%e For a(0) = 11 and A324266(0) = 2, 11^2 + 7 = 128 = 4*2^5.
%p a:=n->11*16807^n: seq(a(n), n=0..20);
%t 11*16807^Range[0,20]
%o (GAP) List([0..20], n->11*16807*n);
%o (Magma) [11*16807^n: n in [0..20]];
%o (PARI) a(n) = 11*16807^n;
%Y Cf. A324266: 2*49^n; A000290: n^2; A000584: n^5; A109808: 2*7^(n-1).
%K nonn,easy
%O 0,1
%A _Stefano Spezia_, Feb 26 2019