A081708 - OEIS

%I #10 Feb 22 2016 11:35:58

%S 2,1,129,193,8449,20801,561537,1892801,37831169,158970433,2580165249,

%T 12754272961,177884848897,994158318401,12378788647809,76004921025473,

%U 868247394485249,5732562340115521,61300395587171457,428184385354564801,4351409702933538049

%N a(n) = a(n-1) + 64*a(n-2) starting with a(0) = 2 and a(1) = 1.

%H Colin Barker, <a href="/A081708/b081708.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 (1,64).

%F a(n) = ((1 + sqrt(257))/2)^n + ((1 - sqrt(257))/2)^n.

%F G.f.: (2-x) / (1-x-64*x^2). - _Colin Barker_, Feb 22 2016

%o (PARI) a(n) = my(w = quadgen(257)); w^n + (1 - w)^n;

%o (PARI) Vec((2-x)/(1-x-64*x^2) + O(x^30)) \\ _Colin Barker_, Feb 22 2016

%Y Cf. A072265.

%K nonn,easy

%O 0,1

%A Helmut Schmiedel (a.positiv(AT)web.de), Apr 03 2003

%E More terms from _Michel Marcus_, Aug 24 2013