A016149 Expansion of g.f. 1/((1 - 4*x)*(1 - 6*x)).
1, 10, 76, 520, 3376, 21280, 131776, 807040, 4907776, 29708800, 179301376, 1080002560, 6496792576, 39047864320, 234555621376, 1408407470080, 8454739787776, 50745618595840, 304542431051776, 1827529464217600, 10966276296933376, 65802055828111360, 394829927154712576
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (10,-24).
Programs
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)))); // Vincenzo Librandi, Jun 24 2013 -
Maple
seq(add(2^(2*n-k)*binomial(n,k)/2,k=1..n),n=1..19); # Zerinvary Lajos, Apr 18 2009
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Mathematica
Join[{a=1,b=10},Table[c=10*b-24*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *) LinearRecurrence[{10,-24},{1,10},30] (* or *) CoefficientList[ Series[ 1/(1-10 x+24 x^2),{x,0,30}],x] (* Harvey P. Dale, Apr 24 2011 *) -
PARI
Vec(1/((1-4*x)*(1-6*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
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SageMath
[lucas_number1(n,10,24) for n in range(1, 20)] # Zerinvary Lajos, Apr 26 2009
Formula
From Barry E. Williams, Jan 13 2000: (Start)
a(n) = 10*a(n-1) - 24*a(n-2) for n>1, a(0)=1.
a(n) = ((6^(n+1)) - 4^(n+1))/2. (End)
a(n) = Sum_{k=0..n} 6^k*4^(n-k). - Bruno Berselli, Aug 07 2013
E.g.f.: exp(4*x)*(3*exp(2*x) - 2). - Stefano Spezia, Jul 23 2024