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a(n) = 4^(floor(n/2))+4^(floor(n/2)-1)-4^(floor((n-1)/3)).
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%I #15 Jul 04 2018 01:56:40

%S 4,4,16,16,76,64,304,304,1216,1216,5056,4864,20224,20224,80896,80896,

%T 326656,323584,1306624,1306624,5226496,5226496,20955136,20905984,

%U 83820544,83820544,335282176,335282176,1341915136,1341128704,5367660544,5367660544,21470642176

%N a(n) = 4^(floor(n/2))+4^(floor(n/2)-1)-4^(floor((n-1)/3)).

%H R. P. Stanley, <a href="https://www.jstor.org/stable/10.4169/000298910x475032">Problem 11348</a>, Amer. Math. Monthly, 117 (2010), 87-88.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,4,0,-16).

%F a(n) = 4*a(n-2)+4*a(n-3)-16*a(n-5). G.f.: -4*x^2*(x^4+4*x^3-x-1) / ((2*x-1)*(2*x+1)*(4*x^3-1)). - _Colin Barker_, Jul 26 2013

%t LinearRecurrence[{0,4,4,0,-16},{4,4,16,16,76},40] (* _Harvey P. Dale_, Mar 11 2017 *)

%Y Cf. A170831, A170832, A170834.

%K nonn,easy

%O 2,1

%A _N. J. A. Sloane_, Dec 30 2009