%I #25 Jan 01 2022 16:09:59
%S 3,0,14,21,98,245,833,2401,7546,22638,69629,211288,645869,1966419,
%T 6000099,18286016,55765626,170002805,518361494,1580379017,4818550093,
%U 14691183577,44792503770,136568135690,416385811429,1269524476220,3870677629833,11801372013543,35981414742371,109704347503632,334479507291398
%N a(n) = (sqrt(7)*csc(Pi/7)/2)^n + (-sqrt(7)*csc(2*Pi/7)/2)^n + (-sqrt(7)*csc(4*Pi/7)/2)^n.
%C (sqrt(7)*csc(Pi/7)/2), (-sqrt(7)*csc(2*Pi/7)/2) and (-sqrt(7)*csc(4*Pi/7)/2) are the roots of the polynomial x^3 - 7*x - 7. - Corrected by _Colin Barker_, Aug 12 2016
%H Colin Barker, <a href="/A275831/b275831.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 (0,7,7).
%F G.f.: (3 - 7*x^2)/(1 - 7*x^2 - 7*x^3). - _Bruno Berselli_, Aug 11 2016
%F a(n) = 7*a(n-2) + 7*a(n-3) with n>2, a(0)=3, a(1)=0, a(2)=14.
%t RecurrenceTable[{a[0] == 3, a[1] == 0, a[2] == 14, a[n] == 7 a[n - 2] + 7 a[n - 3]}, a, {n, 0, 30}] (* _Bruno Berselli_, Aug 11 2016 *)
%t LinearRecurrence[{0,7,7},{3,0,14},40] (* _Harvey P. Dale_, Jan 01 2022 *)
%o (PARI) Vec((3-7*x^2)/(1-7*x^2-7*x^3) + O(x^30)) \\ _Colin Barker_, Aug 12 2016
%Y Cf. A274975, A275195, A275830.
%K nonn,easy
%O 0,1
%A _Kai Wang_, Aug 11 2016
%E Name and comment corrected by _Colin Barker_, Aug 12 2016