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%I #15 Mar 06 2020 13:45:12
%S 2,8,48,320,2176,14848,101376,692224,4726784,32276480,220397568,
%T 1504968704,10276569088,70172803072,479169871872,3271976550400,
%U 22342453428224,152563815022592,1041770892754944,7113656621858816,48575085832830976,331691433687777280
%N a(n) = 2^n*A056236(n).
%C Bhadouria et al. call this the 2-binomial transform of the 2-Lucas numbers.
%H Colin Barker, <a href="/A228568/b228568.txt">Table of n, a(n) for n = 0..1000</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_2.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8).
%F G.f.: 2*( 1-4*x ) / ( 1-8*x+8*x^2 ).
%F a(n) = 2*A084130(n).
%F From _Colin Barker_, Mar 16 2016: (Start)
%F a(n) = ((4-2*sqrt(2))^n+(2*(2+sqrt(2)))^n).
%F a(n) = 8*a(n-1)-8*a(n-2) for n>1.
%F (End)
%o (PARI) Vec(2*(1-4*x)/(1-8*x+8*x^2) + O(x^50)) \\ _Colin Barker_, Mar 16 2016
%K nonn,easy
%O 0,1
%A _R. J. Mathar_, Nov 10 2013
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