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%I #15 Jun 07 2021 04:42:13
%S 1,17689,378225,4109707449,87870152041,954775454112481,
%T 20414169462254569,221815343046210267025,4742660677722035990769,
%U 51532584126226886201833161,1101824413949324675985344641,11972153009151467313136073526409,255978051492792346696545201859225
%N Perfect squares among 17-gonal numbers A051869(k) = k*(15*k - 13)/2.
%C Corresponding square roots sqrt(a(n)) are listed in A137879.
%C Indices of perfect squares among the 17-gonal numbers A051869(k) = k*(15*k - 13)/2 are listed in A137880. Note that all such indices are also perfect squares, their square roots are listed in A137881(k) = sqrt(A137880(k)).
%H Colin Barker, <a href="/A137878/b137878.txt">Table of n, a(n) for n = 1..350</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,232322,-232322,-1,1).
%F a(n) = A137879(n)^2 = A051869( A137880(n) ) = A051869( A137881(n)^2 ).
%F From _Colin Barker_, Jun 19 2016: (Start)
%F a(n) = a(n-1) + 232322*a(n-2) - 232322*a(n-3) - a(n-4) + a(n-5) for n > 5.
%F G.f.: x*(1 + 17688*x + 128214*x^2 + 17688*x^3 + x^4) / ((1-x)*(1 - 482*x + x^2)*(1 + 482*x + x^2)).
%F (End)
%o (PARI) Vec(x*(1+17688*x+128214*x^2+17688*x^3+x^4)/((1-x)*(1-482*x+x^2)*(1+482*x+x^2)) + O(x^20)) \\ _Colin Barker_, Jun 19 2016
%Y Cf. A051869 (17-gonal numbers), A137879, A137880, A137881.
%K nonn,easy
%O 1,2
%A _Alexander Adamchuk_, Feb 19 2008
%E Edited and extended by _Max Alekseyev_, Oct 19 2008