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A135399 a(n) = (-1)^n + (-2)^n + 3^n (-1, -2 and 3 are the roots of the equation x^3 = 7*x + 6).

%I A135399 #18 Jan 05 2021 22:20:00
%S A135399 3,0,14,18,98,210,794,2058,6818,19170,60074,175098,535538,1586130,
%T A135399 4799354,14316138,43112258,129009090,387682634,1161737178,3487832978,
%U A135399 10458256050,31385253914,94134790218,282446313698,847255055010,2541932937194,7625463267258
%N A135399 a(n) = (-1)^n + (-2)^n + 3^n (-1, -2 and 3 are the roots of the equation x^3 = 7*x + 6).
%C A135399 seq(a(3*n+2)/14, n=0..9) = 1, 15, 487, 12507, 342811, 9214935, 249130927, 6723913587, 181566638371, 4902131463855
%C A135399 seq(a(3*n+1)/98, n=0..9) = 0, 1, 21, 613, 16185, 439921, 11854461, 320257693, 8645459745, 233439396841
%C A135399 seq(a(2*n+1)/6, n=0..14) = 0, 3, 35, 343, 3195, 29183, 264355, 2386023, 21501515, 193622863, 1743042675, 15689131703, 141209175835, 1270910544543, 11438306748995
%C A135399 seq(a(6*n+1)/294, n=0..4) = 0, 7, 5395, 3951487, 2881819915
%H A135399 G. C. Greubel, <a href="/A135399/b135399.txt">Table of n, a(n) for n = 0..1000</a>
%H A135399 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,7,6).
%F A135399 G.f.: (3 - 7*x^2)/(1-7*x^2-6*x^3).
%F A135399 E.g.f.: exp(-x) + exp(-2*x) + exp(3*x)
%F A135399 a(0)=3, a(1)=0, a(2)=14, a(n) = 7*a(n-2) + 6*a(n-3). - _Harvey P. Dale_, Oct 18 2015
%e A135399 a(3) = (-1)^3 + (-2)^3 + 3^3 = -1 - 8 + 27 = 18.
%t A135399 Table[(-1)^n+(-2)^n+3^n,{n,0,30}] (* or *) LinearRecurrence[{0,7,6},{3,0,14},30] (* _Harvey P. Dale_, Oct 18 2015 *)
%o A135399 (PARI) a(n)=(-1)^n + (-2)^n + 3^n \\ _Charles R Greathouse IV_, Oct 12 2016
%K A135399 easy,nonn
%O A135399 0,1
%A A135399 _Miklos Kristof_, Dec 11 2007