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a(n) = (4*6^n + (-4)^n)/5.
3

%I #12 Jun 29 2023 18:20:16

%S 1,4,32,160,1088,6016,38144,220672,1356800,8009728,48582656,289398784,

%T 1744781312,10435133440,62745018368,375933239296,2257746919424,

%U 13537891581952,81261709230080,487432816427008,2925146654375936

%N a(n) = (4*6^n + (-4)^n)/5.

%C Binomial transform of A083222.

%H Vincenzo Librandi, <a href="/A083299/b083299.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 (2, 24).

%F a(n) = (4*6^n + (-4)^n)/5.

%F G.f.: (1+2*x)/((1-6*x)*(1+4*x)).

%F E.g.f.: (4*exp(6*x) + exp(-4*x))/5.

%o (Magma) [(4*6^n+(-4)^n)/5: n in [0..25]]; // _Vincenzo Librandi_, Jun 01 2011

%Y Cf. A083300.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 24 2003