cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A248343 a(n) = 10^n - 8^n.

Original entry on oeis.org

0, 2, 36, 488, 5904, 67232, 737856, 7902848, 83222784, 865782272, 8926258176, 91410065408, 931280523264, 9450244186112, 95601953488896, 964815627911168, 9718525023289344, 97748200186314752, 981985601490518016, 9855884811924144128
Offset: 0

Views

Author

Vincenzo Librandi, Oct 05 2014

Keywords

Crossrefs

Programs

  • Magma
    [10^n-8^n: n in [0..30]];
  • Mathematica
    Table[10^n - 8^n, {n, 0, 25}] (* or *) CoefficientList[Series[2 x/((1 - 8 x) (1 - 10 x)), {x, 0, 30}], x]
    LinearRecurrence[{18,-80},{0,2},30] (* Harvey P. Dale, May 21 2018 *)

Formula

G.f.: 2*x/((1-8*x)*(1-10*x)).
a(n) = 18*a(n-1) - 80*a(n-2).
a(n) = 2^n*(5^n - 4^n) = A000079(n)*A005060(n) = A011557(n) - A001018(n).
a(n+1) = 2*A016186(n).
E.g.f.: 2*exp(9*x)*sinh(x). - Elmo R. Oliveira, Mar 31 2025
Showing 1-1 of 1 results.