A281482 - OEIS

%I #15 Sep 08 2022 08:46:18

%S 3,11,39,143,543,2111,8319,33023,131583,525311,2099199,8392703,

%T 33562623,134234111,536903679,2147549183,8590065663,34360000511,

%U 137439477759,549756862463,2199025352703,8796097216511,35184380477439,140737505132543,562949986975743

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

%H Colin Barker, <a href="/A281482/b281482.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 From _Colin Barker_, Jan 22 2017: (Start)

%F a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>2.

%F G.f.: (3 - 10*x + 4*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).

%F (End)

%o (Magma) [2^(n + 1) * (2^n + 1) - 1: n in [0..200]]

%o (PARI) Vec((3 - 10*x + 4*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^30)) \\ _Colin Barker_, Jan 22 2017

%Y Similar sequences: A085601 (2^(n + 1) * (2^n + 1) + 1), A092431 (2^(n - 1) * (2^n + 1) - 1), A092440 (2^(n + 1) * (2^n - 1) + 1), A129868 (2^(n - 1) * (2^n - 1) - 1), A134169 (2^(n - 1) * (2^n - 1) + 1), A267816 (2^(n + 1) * (2^n - 1) - 1), A281481 (2^(n - 1) * (2^n + 1) + 1).

%K nonn,easy

%O 0,1

%A _Jaroslav Krizek_, Jan 22 2017