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%I #21 Nov 12 2024 08:59:53
%S 0,2,20,152,1040,6752,42560,263552,1614080,9815552,59417600,358602752,
%T 2160005120,12993585152,78095728640,469111242752,2816814940160,
%U 16909479575552,101491237191680,609084862103552,3655058928435200,21932552593866752,131604111656222720,789659854309425152,4738099863344906240,28429162130022858752
%N a(n) = 6^n - 4^n.
%H G. C. Greubel, <a href="/A248337/b248337.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-24).
%F G.f.: 2*x/((1-4*x)*(1-6*x)).
%F a(n) = 10*a(n-1) - 24*a(n-2).
%F a(n) = 2^n*(3^n-2^n) = A000079(n) * A001047(n) = A000400(n) - A000302(n).
%F a(n) = 2*A081199(n). - _Bruno Berselli_, Oct 05 2014
%F E.g.f.: 2*exp(5*x)*sinh(x). - _G. C. Greubel_, Nov 11 2024
%t Table[6^n - 4^n, {n,0,30}]
%t CoefficientList[Series[(2 x)/((1-4 x)(1-6 x)), {x, 0, 30}], x]
%t LinearRecurrence[{10,-24},{0,2},30] (* _Harvey P. Dale_, Aug 18 2024 *)
%o (Magma) [6^n-4^n: n in [0..30]];
%o (PARI) vector(20,n,6^(n-1)-4^(n-1)) \\ _Derek Orr_, Oct 05 2014
%o (SageMath)
%o A248337=BinaryRecurrenceSequence(10,-24,0,2)
%o [A248337(n) for n in range(31)] # _G. C. Greubel_, Nov 11 2024
%Y Cf. sequences of the form k^n - 4^n: -A000302 (k=0), -A024036 (k=1), -A020522 (k=2), -A005061 (k=3), A005060 (k=5), this sequence (k=6), A190542 (k=7), A059409 (k=8), A118004 (k=9), A248338 (k=10), A139742 (k=11), 8*A016159 (k=12).
%Y Cf. A000079, A000302, A000400, A001047, A081199.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Oct 05 2014
%E More terms added by _G. C. Greubel_, Nov 11 2024