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%I #23 Jul 04 2022 18:46:58
%S 2,24,448,9216,192512,4030464,84410368,1767899136,37027315712,
%T 775510032384,16242492571648,340187179646976,7124972786941952,
%U 149227367389200384,3125458558976524288,65460453902527758336,1371021545886168645632,28715048051506270961664
%N a(n) = 4^n*A228842(n).
%C Bhadouria et al. call this the 4-binomial transform of the 4-Lucas sequence.
%C Binomial transform of the binomial transform of the binomial transform of A087215.
%H Colin Barker, <a href="/A228843/b228843.txt">Table of n, a(n) for n = 0..750</a>
%H P. Bhadouria, D. Jhala, B. Singh, <a href="http://dx.doi.org/10.22436/jmcs.08.01.07">Binomial Transforms of the k-Lucas Sequences and its Properties</a>, The Journal of Mathematics and Computer Science (JMCS), Volume 8, Issue 1, Pages 81-92; sequence T_4.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24,-64).
%F G.f.: 2*( 1-12*x ) / ( 1-24*x+64*x^2 ).
%F a(n) = 2*A098647(n).
%F a(n) = A000302(n)*A228842(n). - _Omar E. Pol_, Nov 10 2013
%F From _Colin Barker_, Sep 23 2017: (Start)
%F a(n) = 24*a(n-1) - 64*a(n-2) for n>1.
%F a(n) = (12-4*sqrt(5))^n + (4*(3+sqrt(5)))^n.
%F (End)
%t LinearRecurrence[{24,-64},{2,24},20] (* _Harvey P. Dale_, Jul 04 2022 *)
%o (PARI) Vec(2*(1 - 12*x) / (1 - 24*x + 64*x^2 ) + O(x^30)) \\ _Colin Barker_, Sep 23 2017
%K nonn,easy
%O 0,1
%A _R. J. Mathar_, Nov 10 2013