A248338 a(n) = 10^n - 4^n.

0, 6, 84, 936, 9744, 98976, 995904, 9983616, 99934464, 999737856, 9998951424, 99995805696, 999983222784, 9999932891136, 99999731564544, 999998926258176, 9999995705032704, 99999982820130816, 999999931280523264, 9999999725122093056, 99999998900488372224

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 (14,-40).

Crossrefs

Cf. A000079, A000302, A005057, A011557, A016157.

Cf. similar sequences listed in A248337.

Programs

Magma

[10^n-4^n: n in [0..30]];

Mathematica

Table[10^n - 4^n, {n, 0, 30}] (* or *)
CoefficientList[Series[(6 x)/((1-4 x)(1-10 x)), {x, 0, 30}], x]

PARI

vector(20,n,10^(n-1)-4^(n-1)) \\ Derek Orr, Oct 05 2014

Python

def A248338(n): return pow(10,n) - pow(4,n)
print([A248338(n) for n in range(41)]) # G. C. Greubel, Nov 13 2024

Formula

G.f.: 6*x/((1-4*x)*(1-10*x)).

a(n) = 14*a(n-1) - 40*a(n-2).

a(n) = 2^n*(5^n - 2^n) = A000079(n) * A005057(n) = A011557(n) - A000302(n).

a(n+1) = 6*A016157(n). [Bruno Berselli, Oct 05 2014]

E.g.f.: 2*exp(7*x)*sinh(3*x). - G. C. Greubel, Nov 13 2024