A324269 a(n) = 3*11^(2*n).

3, 363, 43923, 5314683, 643076643, 77812273803, 9415285130163, 1139249500749723, 137849189590716483, 16679751940476694443, 2018249984797680027603, 244208248160519283339963, 29549198027422833284135523, 3575452961318162827380398283, 432629808319497702113028192243

Offset

0,1

Comments

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).

Links

Table of n, a(n) for n=0..14.

K. Chakraborty, A. Hoque, R. Sharma, Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations, arXiv:1812.11874 [math.NT], 2018.

Index entries for linear recurrences with constant coefficients, signature (121).

Formula

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

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

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

a(n) = 3*121^n.

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

Example

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

Maple

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

Mathematica

3 121^Range[0, 20]

Prog

(GAP) List([0..20], n->3*121^n);
(Magma) [3*121^n: n in [0..20]];
(PARI) a(n) = 3*121^n;

Crossrefs

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

Sequence in context: A324402 A324427 A304285 * A379758 A173648 A110717

Adjacent sequences: A324266 A324267 A324268 * A324270 A324271 A324272

Keyword

nonn,easy

Author

Stefano Spezia, Feb 27 2019

Status

approved