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%I #25 Jun 04 2020 12:19:16
%S 4,58,988,17560,315184,5669728,102040768,1836676480,33059947264,
%T 595078133248,10711402728448,192805234432000,3470494161055744,
%U 62468894664122368,1124440103014678528,20239921850506117120,364318593294077722624,6557734679233269465088,118039224225958332203008
%N a(n) = 4^n + 3 * 18^n.
%C This sequence is a variation of the sequence A333385, variation proposed by Tony Gardiner in his book in reference.
%C Proposition: a(n) is a perfect square iff n = 0; in this case, a(0) = 4.
%D A. Gardiner, The Mathematical Olympiad Handbook: An Introduction to Problem Solving, Oxford University Press, 1997, reprinted 2011, page 115 (1991).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (22,-72).
%F a(n) = A000302(n) + 3 * A001027(n).
%F a(n) = 22*a(n-1) - 72*a(n-2) for n>1.
%F G.f.: (4 - 30*x)/((1 - 4*x)*(1 - 18*x)). - _Alejandro J. Becerra Jr._, Jun 01 2020
%e a(4) = 4^4 + 3 * 18^4 = 315184 = 2^4 * 19699 is not a perfect square.
%p S:=seq(4^n+3*18^n, n=0..20);
%Y Cf. A000302, A001027, A333385.
%K nonn,easy
%O 0,1
%A _Bernard Schott_, May 18 2020