A324265 -id:A324265 - cp's OEIS frontend

2, 98, 4802, 235298, 11529602, 564950498, 27682574402, 1356446145698, 66465861139202, 3256827195820898, 159584532595224002, 7819642097165976098, 383162462761132828802, 18774960675295508611298, 919973073089479921953602, 45078680581384516175726498, 2208855348487841292610598402

Offset: 0

Stefano Spezia, Feb 20 2019

x = A324265(n) and y = a(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 7^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma).

			For A324265(0) = 5 and a(0) = 2, 5^2 + 7 = 32 = 4*2^3.

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

Cf. A324265 (5*343^n), A000290 (n^2), A000578 (n^3), A109808 (2*7^(n-1)).

GAP
```
List([0..20], n->2*49^n);
```
Magma
```
[2*49^n: n in [0..20]];
```
Maple
```
a:=n->2*49^n: seq(a(n), n=0..20);
```
Mathematica
```
2*49^Range[0,20]
```
PARI
```
a(n) = 2*49^n;
```

O.g.f.: 2/(1 - 49*x).
E.g.f.: 2*exp(49*x).
a(n) = 49*a(n-1) for n > 0.
a(n) = (49/2)*(A109808(n))^2.

cp's OEIS Frontend

A324266 a(n) = 2*49^n.

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