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%I #35 Feb 02 2024 19:24:49
%S 4,18,70,270,1054,4158,16510,65790,262654,1049598,4196350,16781310,
%T 67117054,268451838,1073774590,4295032830,17180000254,68719738878,
%U 274878431230,1099512676350,4398048608254,17592190238718,70368752566270,281474993487870,1125899940397054
%N a(n) = 2*(2^n + 1)*(2^(n+1) - 1).
%H G. C. Greubel, <a href="/A005367/b005367.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F G.f.: 2*(2 - 5*x)/((1 - x)*(1 - 2*x)*(1 - 4*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%F From _G. C. Greubel_, Oct 21 2017: (Start)
%F E.g.f.: 2*exp(x)*(2*exp(3*x) + exp(x) - 1).
%F a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3). (End)
%F a(n) = 2 * A092431(n+1). - _Alois P. Heinz_, Feb 02 2024
%F a(n) = 4^(n+1) + 2^(n+1) - 2. - _Ramzan Guekhaev_, Feb 02 2024
%t Table[2*(2^n + 1)*(2^(n + 1) - 1), {n, 0, 50}] (* _G. C. Greubel_, Oct 21 2017 *)
%o (PARI) for(n=0,50, print1(2*(2^n + 1)*(2^(n + 1) - 1), ", ")) \\ _G. C. Greubel_, Oct 21 2017
%o (Magma) [2*(2^n + 1)*(2^(n + 1) - 1): n in [0..50]]; // _G. C. Greubel_, Oct 21 2017
%Y Cf. A092431.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E An incorrect g.f. was deleted by _N. J. A. Sloane_, Sep 20 2008
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