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

0,2

Comments

Binomial transform of A083296.

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).

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

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

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 *)

Prog

(Magma) [(4*4^n+(-6)^n)/5: n in [0..30]]; // Vincenzo Librandi, Jun 08 2011
(PARI) first(n) = Vec((1+4*x)/((1-4*x)*(1+6*x)) + O(x^n)) \\ Iain Fox, Oct 31 2018
(PARI) a(n) = (4*4^n + (-6)^n)/5 \\ Iain Fox, Oct 31 2018
(GAP) List([0..25], n->(4*4^n+(-6)^n)/5); # Muniru A Asiru, Oct 31 2018

Crossrefs

Cf. A083222.

Sequence in context: A076495 A308387 A058403 * A343927 A221921 A012739

Adjacent sequences: A083294 A083295 A083296 * A083298 A083299 A083300

Keyword

easy,sign

Author

Paul Barry, Apr 24 2003

Status

approved