A083297 a(n) = (4*4^n + (-6)^n)/5.
1, 2, 20, 8, 464, -736, 12608, -42880, 388352, -1805824, 12932096, -69203968, 448778240, -2558451712, 15887581184, -93178003456, 567657955328, -3371587993600, 20366966915072, -121652045676544, 732111297314816, -4383871690866688, 26338414517288960
Offset: 0
Links
- Iain Fox, Table of n, a(n) for n = 0..1000 (terms 0..300 from Vincenzo Librandi)
- Index entries for linear recurrences with constant coefficients, signature (-2,24).
Crossrefs
Cf. A083222.
Programs
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GAP
List([0..25],n->(4*4^n+(-6)^n)/5); # Muniru A Asiru, Oct 31 2018
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Magma
[(4*4^n+(-6)^n)/5: n in [0..30]]; // Vincenzo Librandi, Jun 08 2011
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Maple
seq(coeff(series((1+4*x)/((1-4*x)*(1+6*x)),x,n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 31 2018
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Mathematica
CoefficientList[Series[(1 + 4 x)/((1 - 4 x) (1 + 6 x)), {x, 0, 22}], x] (* Michael De Vlieger, Oct 31 2018 *) CoefficientList[Series[(4*Exp[4*x] + Exp[-6*x])/5, {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Nov 01 2018 *) LinearRecurrence[{-2,24}, {1,2}, 30] (* G. C. Greubel, Nov 07 2018 *) -
PARI
first(n) = Vec((1+4*x)/((1-4*x)*(1+6*x)) + O(x^n)) \\ Iain Fox, Oct 31 2018
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PARI
a(n) = (4*4^n + (-6)^n)/5 \\ Iain Fox, Oct 31 2018
Formula
a(n) = (4*4^n + (-6)^n)/5.
G.f.: (1+4*x)/((1-4*x)*(1+6*x)).
E.g.f.: (4*exp(4*x) + exp(-6*x))/5.
a(n) = -2*a(n-1) + 24*a(n-2). - Iain Fox, Oct 31 2018
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