A324269 - OEIS

%I #12 Sep 08 2022 08:46:24

%S 3,363,43923,5314683,643076643,77812273803,9415285130163,

%T 1139249500749723,137849189590716483,16679751940476694443,

%U 2018249984797680027603,244208248160519283339963,29549198027422833284135523,3575452961318162827380398283,432629808319497702113028192243

%N a(n) = 3*11^(2*n).

%C x = A324268(n) and y = a(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 11^(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 (121).

%F O.g.f.: 3/(1 - 121*x).

%F E.g.f.: 3*exp(121*x).

%F a(n) = 121*a(n-1) for n > 0.

%F a(n) = 3*121^n.

%F a(n) = 3*A001020(n)^2.

%e For A324268(0) = 31 and a(0) = 3, 31^2 + 11 = 972 = 4*3^5.

%p a:=n->3*121^n: seq(a(n), n=0..20);

%t 3 121^Range[0, 20]

%o (GAP) List([0..20], n->3*121^n);

%o (Magma) [3*121^n: n in [0..20]];

%o (PARI) a(n) = 3*121^n;

%Y Cf. A324268: 31*11^(5*n); A000290: n^2; A000584: n^5; A001020: 11^n.

%K nonn,easy

%O 0,1

%A _Stefano Spezia_, Feb 27 2019