|
%I #34 Nov 08 2023 12:43:52
%S 10,11,13,17,25,41,73,137,265,521,1033,2057,4105,8201,16393,32777,
%T 65545,131081,262153,524297,1048585,2097161,4194313,8388617,16777225,
%U 33554441,67108873,134217737,268435465,536870921,1073741833,2147483657,4294967305
%N a(n) = 2^n + 9.
%H Vincenzo Librandi, <a href="/A188165/b188165.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Bruno Berselli_, Sep 26 2011: (Start)
%F G.f.: (10-19*x)/(1-3*x+2*x^2).
%F a(n) = 2*a(n-1)-9 = 3*a(n-1)-2*a(n-2).
%F a(n) = A168415(n)+2. (End)
%F E.g.f.: exp(2*x) + 9*exp(x). - _Elmo R. Oliveira_, Nov 08 2023
%t Table[2^n + 9, {n, 0, 40}] (* or *) CoefficientList[Series[(10 - 19 x)/((1 - x) (1 - 2 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, May 13 2014 *)
%o (PARI) a(n) = 1<<n + 9 \\ _Michel Marcus_, Jul 19 2013
%o (Magma) [2^n+9: n in [0..40]]; // _Vincenzo Librandi_, May 13 2014
%Y Cf. A000079, A104070 (primes of this form), A168415.
%K nonn,easy
%O 0,1
%A _Brad Clardy_, Mar 23 2011
|
