A304723 a(n) = 5^(n-1)*(3^n - 1)/2.

0, 1, 20, 325, 5000, 75625, 1137500, 17078125, 256250000, 3844140625, 57664062500, 864970703125, 12974609375000, 194619384765625, 2919291992187500, 43789385986328125, 656840820312500000, 9852612457275390625, 147789187622070312500, 2216837818145751953125, 33252567291259765625000

Offset: 0

Author

Vincenzo Librandi, May 22 2018

Keywords

• nonn
• easy

Comments

It is easy to prove that when a(n) is divisible by 7 it is also divisible by 13, but the converse does not always hold. - Bruno Berselli, May 22 2018

Links

• Stephan Ramon Garcia, Yu Xuan Hong, Florian Luca, Elena Pinsker, Carlo Sanna, Evan Schechter and Adam Starr, p-Adic Quotient Sets, arXiv:1607.07951 [math.NT], 2018 (see Example 5.5, page 15).
• Index entries for linear recurrences with constant coefficients, signature (20,-75).

Crossrefs

Subsequence of A047239 (after 0).

Programs

Magma

[5^(n-1)*(3^n-1)/2: n in [0..20]];

Mathematica

Table[5^(n - 1) (3^n - 1)/2, {n, 0, 25}]

PARI

a(n) = 5^(n-1) * (3^n - 1) / 2 \\ Felix Fröhlich, May 22 2018

Formula

O.g.f.: x/((1 - 5*x)*(1 - 15*x)).

E.g.f.: (-1 + exp(10*x))*exp(5*x)/10. - Bruno Berselli, May 22 2018

a(n) = 20*a(n-1) - 75*a(n-2), n>1.