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A137881 a(n) = sqrt(A137880(n)).

%I A137881 #23 Sep 08 2022 08:45:33
%S A137881 1,7,15,153,329,3359,7223,73745,158577,1619031,3481471,35544937,
%T A137881 76433785,780369583,1678061799,17132585889,36840925793,376136519975,
%U A137881 808822305647,8257870853561,17757249798441,181297022258367,389850673260055,3980276618830513,8558957561922769
%N A137881 a(n) = sqrt(A137880(n)).
%C A137881 A137880 gives the indices m (= a(n)^2) of perfect squares in 17-gonal numbers A051869(m) = m(15m -13)/2. Corresponding 17-gonal numbers are listed in A137878(n) = A051869( a(n)^2 ).
%C A137881 Positive values of x (or y) satisfying x^2 - 22xy + y^2 + 104 = 0. - _Colin Barker_, Feb 19 2014
%H A137881 Vincenzo Librandi, <a href="/A137881/b137881.txt">Table of n, a(n) for n = 1..200</a>
%H A137881 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,22,0,-1).
%F A137881 a(n) = sqrt(A137880(n)). A051869( a(n)^2 ) = A137878(n).
%F A137881 For n>=5, a(n) = 22*a(n-2) - a(n-4). [Alekseyev]
%F A137881 a(2n) = (15 - sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 + sqrt(30))/30 * (11 - 2*sqrt(30))^n. [Alekseyev]
%F A137881 a(2n+1) = (15 + sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 - sqrt(30))/30 * (11 - 2*sqrt(30))^n. [Alekseyev]
%F A137881 G.f.: -x*(x-1)*(x^2+8*x+1) / (x^4-22*x^2+1). - _Colin Barker_, Feb 19 2014
%t A137881 CoefficientList[Series[(1 - x) (x^2 + 8 x + 1)/(x^4 - 22 x^2 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 21 2014 *)
%o A137881 (Magma) I:=[1,7,15,153]; [n le 4 select I[n] else 22*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Feb 21 2014
%Y A137881 Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137879, A137880.
%K A137881 nonn,easy
%O A137881 1,2
%A A137881 _Alexander Adamchuk_, Feb 19 2008
%E A137881 Edited and extended by _Max Alekseyev_, Oct 19 2008