A248226 a(n) = 10^n - 3^n.

0, 7, 91, 973, 9919, 99757, 999271, 9997813, 99993439, 999980317, 9999940951, 99999822853, 999999468559, 9999998405677, 99999995217031, 999999985651093, 9999999956953279, 99999999870859837, 999999999612579511, 9999999998837738533, 99999999996513215599

Offset: 0

Author

Vincenzo Librandi, Oct 05 2014

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (13,-30).

Crossrefs

Cf. similar sequences listed in A248225.

Cf. A016145, A016189.

Programs

Magma

[10^n-3^n: n in [0..30]];

Mathematica

Table[10^n - 3^n, {n, 0, 25}] (* or *) CoefficientList[Series[(7 x)/((1 - 3 x) (1 - 10 x)), {x, 0, 30}], x]
LinearRecurrence[{13,-30},{0,7},30] (* Harvey P. Dale, Jul 10 2021 *)

PARI

a(n) = 10^n - 3^n \\ Michel Marcus, Oct 05 2014

Formula

G.f.: 7*x/((1 - 3*x)*(1 - 10*x)).

a(n) = 13*a(n-1) - 30*a(n-2).

a(n) = A011557(n) - A000244(n).

a(2*n) mod 10^n = A016189(n). - Michel Marcus, Oct 05 2014

a(n+1) = 7*A016145(n). - Bruno Berselli, Oct 05 2014

E.g.f.: exp(3*x)*(exp(7*x) - 1). - Stefano Spezia, Mar 09 2025