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a(n) = (4*8^n + (-2)^n)/5.
3

%I #28 Sep 08 2022 08:45:10

%S 1,6,52,408,3280,26208,209728,1677696,13421824,107374080,858993664,

%T 6871947264,54975582208,439804649472,3518437212160,28147497664512,

%U 225179981381632,1801439850921984,14411518807638016,115292150460579840

%N a(n) = (4*8^n + (-2)^n)/5.

%C Binomial transform of A083300.

%H Vincenzo Librandi, <a href="/A083301/b083301.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,16).

%F G.f.: 1/((1-8*x)(1+2*x)).

%F E.g.f.: (4*exp(8*x) + exp(-2*x))/5.

%t Table[(4 * 8^n + (-2)^n)/5, {n, 0, 19}] (* _Alonso del Arte_, Mar 29 2011 *)

%o (Sage) [lucas_number1(n,6,-16) for n in range(1, 21)] # _Zerinvary Lajos_, Apr 24 2009

%o (Magma) [(4*8^n+(-2)^n)/5: n in [0..25]]; // _Vincenzo Librandi_, Jun 29 2011

%o (PARI) a(n)=4^(n+1)\/5<<n \\ _Charles R Greathouse IV_, Jun 29 2011

%Y Cf. A083302.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 24 2003