%I #28 Jul 05 2024 14:02:53

%S 2,10,108,982,8120,65426,524132,4194094,33554160,268435114,2147483228,

%T 17179868678,137438952872,1099511627074,8796093021396,70368744176734,

%U 562949953420256,4503599627369306,36028797018962636

%N a(n) = 2^(3*n+1) - 2*n*(2*n+1).

%H Vincenzo Librandi, <a href="/A003222/b003222.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-27,25,-8).

%F From _R. J. Mathar_, May 05 2010: (Start)

%F a(n) = 11*a(n-1) - 27*a(n-2) + 25*a(n-3) - 8*a(n-4).

%F G.f.: 2*(1 - 6*x + 26*x^2 + 7*x^3)/ ( (8*x-1)* (x-1)^3). (End)

%o (Magma) [2^(3*n+1)-2*n*(2*n+1): n in [0..20]]; // _Vincenzo Librandi_, Jun 26 2011

%o (PARI) a(n) = 2^(3*n+1)-2*n*(2*n+1); \\ _Altug Alkan_, Sep 21 2018

%Y Equals A013730-A002943.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_