A248340 a(n) = 10^n - 5^n.

0, 5, 75, 875, 9375, 96875, 984375, 9921875, 99609375, 998046875, 9990234375, 99951171875, 999755859375, 9998779296875, 99993896484375, 999969482421875, 9999847412109375, 99999237060546875, 999996185302734375, 9999980926513671875

Offset: 0

Author

Vincenzo Librandi, Oct 05 2014

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..995
• Index entries for linear recurrences with constant coefficients, signature (15,-50).

Crossrefs

Cf. sequences of the form k^n-5^n: A005062 (k=6), A121213 (k=7), A191468 (k=8), A191466 (k=9), this sequence (k=10), A139743 (k=11).

Cf. A000225, A000351, A011557, A016164.

Programs

Magma

[10^n-5^n: n in [0..30]];

Mathematica

Table[10^n - 5^n, {n,0,30}]
CoefficientList[Series[5 x/((1-5 x)(1-10 x)), {x, 0, 30}], x]

Python

def A248340(n): return pow(10,n) - pow(5,n)
print([A248340(n) for n in range(41)]) # G. C. Greubel, Nov 13 2024

Formula

G.f.: 5*x/((1-5*x)*(1-10*x)).

a(n) = 15*a(n-1) - 50*a(n-2).

a(n) = 5^n*(2^n-1) = A000351(n) * A000225(n) = A011557(n) - A000351(n).

a(n) = 5*A016164(n-1).

a(n) = A016164(n) - A011557(n).

E.g.f.: exp(10*x) - exp(5*x). - G. C. Greubel, Nov 13 2024