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a(n) = (n-1)*2^n - 1.
1

%I #13 Dec 21 2016 02:43:21

%S -1,3,15,47,127,319,767,1791,4095,9215,20479,45055,98303,212991,

%T 458751,983039,2097151,4456447,9437183,19922943,41943039,88080383,

%U 184549375,385875967,805306367,1677721599,3489660927,7247757311,15032385535

%N a(n) = (n-1)*2^n - 1.

%C Prime for n = 2, 4, 5, 11, 28, 35, no more < 100.

%H G. C. Greubel, <a href="/A163383/b163383.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, -8, 4).

%F a(n) = A000337(n) - 2.

%F From _R. J. Mathar_, Jul 26 2009: (Start)

%F a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3).

%F G.f.: x*(1-8*x+8*x^2)/((x-1)*(-1+2*x)^2). (End)

%e a(28) = ((2^(28))*(28 - 1)) - 1 = 7247757311.

%t LinearRecurrence[{5, -8, 4}, {-1, 3, 15}, 100] (* _G. C. Greubel_, Dec 20 2016 *)

%o (PARI) Vec(x*(1-8*x+8*x^2)/((x-1)*(-1+2*x)^2) + O(x^50)) \\ _G. C. Greubel_, Dec 20 2016

%Y Cf. A000337.

%K easy,sign

%O 1,2

%A _Jonathan Vos Post_, Jul 25 2009