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%I #29 Sep 08 2022 08:46:04
%S 0,1,1,5,22,13,52,204,113,435,1667,910,3471,13224,7192,27367,104105,
%T 56563,215098,817909,444276,1689212,6422529,3488381,13262821,50424942,
%U 27387681,104126704,395884336,215018609,817488295,3108041875,1688083894,6417991803,24400809980
%N a(n) = A(n)*7^(-floor(n+1)/3), where A(n) = 7*A(n-1) - 14*A(n-2) + 7*A(n-3) with A(0)=0, A(1)=1, A(2)=7.
%C The Berndt-type sequence number 18a for the argument 2Pi/7, which is closely connected with the sequence A217274. Definitions other Berndt-type sequences for the argument 2Pi/7 like A215575, A215877, A033304 in sequences from Crossrefs are given.
%H Vincenzo Librandi, <a href="/A217444/b217444.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,10,0,0,-17,0,0,1).
%F G.f.: x*(1+x+5*x^2+12*x^3+3*x^4+2*x^5+x^6)/(1-10*x^3+17*x^6-x^9). - _Bruno Berselli_, Oct 03 2012
%F a(n) = 10*a(n-3) - 17*a(n-6) + a(n-9). - _G. C. Greubel_, Apr 23 2018
%t CoefficientList[Series[x*(1+x+5*x^2+12*x^3+3*x^4+2*x^5+x^6)/(1 - 10*x^3 + 17*x^6 - x^9), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 15 2012 *)
%t LinearRecurrence[{0,0,10,0,0,-17,0,0,1}, {0, 1, 1, 5, 22, 13, 52, 204, 113}, 50] (* _G. C. Greubel_, Apr 23 2018 *)
%o (Magma) i:=35; I:=[0, 1, 7]; A:=[m le 3 select I[m] else 7*Self(m-1)-14*Self(m-2)+7*Self(m-3): m in [1..i]]; [7^(-Floor(n/3))*A[n]: n in [1..i]]; // _Bruno Berselli_, Oct 03 2012
%o (PARI) x='x+O('x^30); concat([0], Vec(x*(1+x+5*x^2+12*x^3+3*x^4 +2*x^5 +x^6)/(1- 10*x^3+17*x^6-x^9))) \\ _G. C. Greubel_, Apr 23 2018
%Y Cf. A215007, A215008, A215143, A215493, A215494, A215510, A215512, A215575, A215694, A215695, A108716, A215794, A215828, A215817, A215877, A094429, A094430, A217274, A094648, A033304.
%K nonn,easy
%O 0,4
%A _Roman Witula_, Oct 03 2012
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