A019333 Expansion of g.f. 1/((1-4*x)*(1-6*x)*(1-8*x)).
1, 18, 220, 2280, 21616, 194208, 1685440, 14290560, 119232256, 983566848, 8047836160, 65462691840, 530198327296, 4280634482688, 34479631482880, 277245459333120, 2226418414452736, 17862092934217728, 143201285904793600, 1147437816702566400, 9190468809917464576
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (18,-104,192).
Programs
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Magma
m:=20; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-8*x)))); // Vincenzo Librandi, Jul 02 2013 -
Magma
I:=[1, 18, 220]; [n le 3 select I[n] else 18*Self(n-1)-104*Self(n-2)+192*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013
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Mathematica
CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *) -
PARI
Vec(1/((1-4*x)*(1-6*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
Formula
a(n) = 2*4^n -9*6^n +8*8^n. - R. J. Mathar, Jun 29 2013
From Vincenzo Librandi, Jul 02 2013: (Start)
a(n) = 18*a(n-1) - 104*a(n-2) + 192*a(n-3) for n > 2.
a(n) = 14*a(n-1) - 48*a(n-2) + 4^n. (End)
E.g.f.: exp(4*x)*(2 - 9*exp(2*x) + 8*exp(4*x)). - Stefano Spezia, Jun 04 2024
From Seiichi Manyama, May 04 2025: (Start)
a(n) = Sum_{k=0..n} 2^k * 4^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).
a(n) = Sum_{k=0..n} (-2)^k * 8^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2). (End)