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%I #17 Sep 08 2022 08:46:16
%S 0,4,32,252,1984,15620,122976,968188,7622528,60012036,472473760,
%T 3719778044,29285750592,230566226692,1815244062944,14291386276860,
%U 112515846151936,885835382938628,6974167217357088,54907502355918076,432285851629987520,3403379310683982084
%N Numbers n such that 15*n^2 + 16 is a square.
%H Colin Barker, <a href="/A273053/b273053.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-1).
%F O.g.f.: 4*x^2/(1 - 8*x + x^2).
%F E.g.f.: 4*(1 + (4*sqrt(15)*sinh(sqrt(15)*x) - 15*cosh(sqrt(15)*x))*exp(4*x)/15). - _Ilya Gutkovskiy_, May 14 2016
%F a(n) = 8*a(n-1) - a(n-2) for n>2.
%F a(n) = -(2*((4-sqrt(15))^n*(4+sqrt(15))+(-4+sqrt(15))*(4+sqrt(15))^n))/sqrt(15). - _Colin Barker_, May 14 2016
%F a(n+2) - a(n+1) = 4*070997(n) for n>0. - _Wesley Ivan Hurt_, May 14 2016
%p a:=proc(n) option remember; if n=1 then 0 elif n=2 then 4 else 8*a(n-1) - a(n-2); fi; end: seq(a(n), n=1..30); # _Wesley Ivan Hurt_, May 14 2016
%t LinearRecurrence[{8, -1}, {0, 4}, 30]
%o (Magma) [n: n in [0..2*10^7] |IsSquare(15*n^2+16)];
%o (PARI) concat(0, Vec(4*x^2/(1-8*x+x^2) + O(x^50))) \\ _Colin Barker_, May 14 2016
%Y Cf. A070997, similar sequences listed in A273052.
%K nonn,easy
%O 1,2
%A _Vincenzo Librandi_, May 14 2016
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