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a(n) = 11*7^(5*n).
0

%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