A016188 Expansion of 1/((1-8*x)*(1-12*x)).

1, 20, 304, 4160, 54016, 680960, 8433664, 103301120, 1256390656, 15210905600, 183604609024, 2211845242880, 26610862391296, 319880104509440, 3842959300624384, 46150695979581440, 554089826731687936, 6651329720593940480, 79833971045636767744, 958151767735717068800

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (20,-96).

Crossrefs

Cf. A016140.

Programs

Magma

[4^n*(3^(n+1)-2^(n+1)): n in [0..40]]; // G. C. Greubel, Nov 14 2024

Mathematica

A016188[n_] := 3*12^n - 2*8^n; Array[A016188, 20, 0] (*  or *)
LinearRecurrence[{20, -96}, {1, 20}, 20] (* Paolo Xausa, Feb 08 2024 *)

SageMath

A016188=BinaryRecurrenceSequence(20,-96,1,20)
print([A016188(n) for n in range(41)]) # G. C. Greubel, Nov 14 2024

Formula

a(n) = 3*12^n - 2*8^n. - Bruno Berselli, Feb 09 2011

a(n) = 12*a(n-1) + 8^n, a(0)=1. - Vincenzo Librandi, Feb 09 2011

a(n) = 20*a(n-1) - 96*a(n-2), a(0)=1, a(1)=20. - Vincenzo Librandi, Feb 09 2011

E.g.f.: 3*exp(12*x) - 2*exp(8*x). - G. C. Greubel, Nov 14 2024