A016140 Expansion of 1/((1-3*x)*(1-8*x)).
1, 11, 97, 803, 6505, 52283, 418993, 3354131, 26839609, 214736555, 1717951489, 13743789059, 109950843913, 879608345627, 7036871547985, 56294986732787, 450359936909017, 3602879624412299, 28823037382718881, 230584300224012515, 1844674405278884521, 14757395252691429371, 118059162052912494577, 944473296517443135443
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (11,-24).
Crossrefs
Programs
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-8*x)))); // Vincenzo Librandi, Jun 24 2013 -
Mathematica
Table[(8^(n+1)-3^(n+1))/5, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2011 *) CoefficientList[Series[1/((1-3 x)(1-8 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 24 2013 *) LinearRecurrence[{11,-24},{1,11},30] (* Harvey P. Dale, Feb 03 2022 *) -
PARI
Vec(1/((1-3*x)*(1-8*x))+O(x^30)) \\ Charles R Greathouse IV, Sep 23 2012
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Sage
[lucas_number1(n,11,24) for n in range(1, 30)] # Zerinvary Lajos, Apr 27 2009
Formula
a(n) = (8^(n+1) - 3^(n+1))/5.
a(n) = 11*a(n-1) - 24*a(n-2).
a(n) = 3*a(n-1) + 8^n.
a(n) = 8*a(n-1) + 3^n.
a(n) = Sum_{i=0..n} 3^i*8^(n-i).
E.g.f.: (1/5)*(8*exp(8*x) - 3*exp(3*x)). - G. C. Greubel, Nov 14 2024
Comments