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a(n) = 5*a(n-2) + 2*a(n-3).
2

%I #22 Sep 25 2024 23:13:08

%S 1,2,4,12,24,68,144,388,856,2228,5056,12852,29736,74372,174384,431332,

%T 1020664,2505428,5965984,14568468,34840776,84774308,203340816,

%U 493553092,1186252696,2874447092,6918369664,16744740852,40340742504,97560443588

%N a(n) = 5*a(n-2) + 2*a(n-3).

%H Harvey P. Dale, <a href="/A135139/b135139.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 (0, 5, 2).

%F From _R. J. Mathar_, Feb 15 2008: (Start)

%F O.g.f.: 4*(x-2)/(7*(x^2+2*x-1)) - 1/(7*(1+2*x)).

%F a(n) = (4*A078343(n+1)-(-2)^n)/7.

%F a(n) = A135138(n+2) + 2*A135138(n+1) - A135138(n). (End)

%t a = {1, 2, 4}; Do[AppendTo[a, 5*a[[ -2]] + 2*a[[ -3]]], {40}]; a (* _Stefan Steinerberger_, Feb 15 2008 *)

%t LinearRecurrence[{0,5,2},{1,2,4},30] (* _Harvey P. Dale_, May 25 2012 *)

%Y Cf. A135138.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Feb 13 2008

%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Feb 15 2008