A306472 a(n) = 37*27^n.

37, 999, 26973, 728271, 19663317, 530909559, 14334558093, 387033068511, 10449892849797, 282147106944519, 7617971887502013, 205685240962554351, 5553501505988967477, 149944540661702121879, 4048502597865957290733, 109309570142380846849791, 2951358393844282864944357

Offset: 0

Author

Stefano Spezia, Feb 18 2019

Keywords

• nonn
• easy

Comments

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).

Examples

			For a(0) = 37 and A002042(0) = 7, 37^2 + 3 = 1372 = 4*7^3.
		

Links

• K. Chakraborty, A. Hoque, and 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 (27).

Crossrefs

Cf. A002042 (7*4^n), A009971 (27^n), A000290 (n^2), A000578 (n^3).

Programs

GAP

List([0..20], n->37*27^n);

Magma

[37*27^n: n in [0..20]];

Maple

a:=n->37*27^n: seq(a(n), n=0..20);

Mathematica

37*27^Range[0,20]

PARI

a(n) = 37*27^n;

Formula

O.g.f.: 37/(1 - 27*x).

E.g.f.: 37*exp(27*x).

a(n) = 27*a(n-1) for n > 0.

a(n) = 37*A009971(n).