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A248216 a(n) = 6^n - 2^n.

%I A248216 #22 Mar 27 2022 13:39:32
%S A248216 0,4,32,208,1280,7744,46592,279808,1679360,10077184,60465152,
%T A248216 362795008,2176778240,13060685824,78364147712,470184951808,
%U A248216 2821109841920,16926659313664,101559956406272,609359739486208,3656158439014400,21936950638280704
%N A248216 a(n) = 6^n - 2^n.
%H A248216 G. C. Greubel, <a href="/A248216/b248216.txt">Table of n, a(n) for n = 0..1000</a>
%H A248216 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-12).
%F A248216 G.f.: 4*x/((1-2*x)*(1-6*x)).
%F A248216 a(n) = 8*a(n-1) - 12*a(n-2).
%F A248216 a(n) = 2^n*(3^n - 1) = A000079(n) * A024023(n).
%F A248216 E.g.f.: exp(6*x) - exp(2*x) = 2*exp(4*x)*sinh(2*x). - _G. C. Greubel_, Feb 09 2021
%F A248216 a(n) = 4*A016129(n-1). - _R. J. Mathar_, Mar 10 2022
%F A248216 a(n) = A000400(n) - A000079(n). - _Bernard Schott_, Mar 27 2022
%t A248216 Table[6^n - 2^n, {n, 0, 25}] (* or *) CoefficientList[Series[4x/((1-2x)(1-6x)), {x, 0, 30}], x]
%t A248216 LinearRecurrence[{8,-12},{0,4},30] (* _Harvey P. Dale_, Dec 21 2019 *)
%o A248216 (Magma) [6^n-2^n: n in [0..25]];
%o A248216 (Sage) [2^n*(3^n -1) for n in (0..25)] # _G. C. Greubel_, Feb 09 2021
%Y A248216 Sequences of the form k^n - 2^n: A001047 (k=3), A020522 (k=4), A005057 (k=5), this sequence (k=6), A190540 (k=7), A248217 (k=8), A191465 (k=9), A060458 (k=10), A139740 (k=11).
%Y A248216 Cf. A000079, A000400, A024023.
%K A248216 nonn,easy
%O A248216 0,2
%A A248216 _Vincenzo Librandi_, Oct 04 2014