A090591 Expansion of g.f.: 1/(1 - 2*x + 8*x^2).
1, 2, -4, -24, -16, 160, 448, -384, -4352, -5632, 23552, 92160, -4096, -745472, -1458176, 3047424, 17760256, 11141120, -119799808, -328728576, 300941312, 3231711232, 4055891968, -17741905920, -67930947584
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-8).
Programs
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GAP
a:=[1,2];; for n in [3..30] do a[n]:=2*a[n-1]-8*a[n-2]; od; a; # Muniru A Asiru, Oct 23 2018
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Magma
[n le 2 select n else 2*Self(n-1) - 8*Self(n-2): n in [1..30]]; // G. C. Greubel, Oct 22 2018
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Maple
seq(coeff(series(1/(1-2*x+8*x^2),x,n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 23 2018
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Mathematica
LinearRecurrence[{2,-8}, {1,2}, 30] (* G. C. Greubel, Oct 22 2018 *) CoefficientList[Series[1/(1-2x+8x^2),{x,0,60}],x] (* Harvey P. Dale, Jan 17 2021 *) -
PARI
x='x+O('x^30); Vec(1/(1 - 2*x + 8*x^2)) \\ G. C. Greubel, Oct 22 2018 -
Sage
[lucas_number1(n,2,8) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009
Formula
Binomial transform of (1+x)/(1+7*x^2).
a(0)=1, a(1)=2, a(n) = 2*a(n-1) - 8*a(n-2) for n>1. - Philippe Deléham, Sep 19 2009
Extensions
Formulae from Paul Barry, Dec 05 2003
Corrected by T. D. Noe, Dec 11 2006
Comments