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

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (20,-96).

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

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 *)

Prog

(Magma) [4^n*(3^(n+1)-2^(n+1)): n in [0..40]]; // G. C. Greubel, Nov 14 2024
(SageMath)
A016188=BinaryRecurrenceSequence(20, -96, 1, 20)
print([A016188(n) for n in range(41)]) # G. C. Greubel, Nov 14 2024

Crossrefs

Cf. A016140.

Sequence in context: A001755 A361577 A016190 * A006300 A282372 A361293

Adjacent sequences: A016185 A016186 A016187 * A016189 A016190 A016191

Keyword

nonn,changed

Author

N. J. A. Sloane

Status

approved