%I #26 Sep 03 2019 09:54:46

%S 3,4,5,9,12,23,31,60,81,157,212,411,555,1076,1453,2817,3804,7375,9959,

%T 19308,26073,50549,68260,132339,178707,346468,467861,907065,1224876,

%U 2374727,3206767,6217116,8395425,16276621,21979508,42612747,57543099,111561620

%N Values of x in the solutions to x^2 - 3xy + y^2 + 11 = 0, where 0 < x < y.

%C The corresponding values of y are given by a(n+2).

%C Positive values of x (or y) satisfying x^2 - 18xy + y^2 + 704 = 0.

%H Colin Barker, <a href="/A237132/b237132.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).

%F a(n) = 3*a(n-2)-a(n-4).

%F G.f.: -x*(x-1)*(3*x^2+7*x+3) / ((x^2-x-1)*(x^2+x-1)).

%F a(n) = F(n+2) + (-1)^n*F(n-3), n>1, with F the Fibonacci numbers (A000045). - _Ralf Stephan_, Feb 05 2014

%F Let h(n) = hypergeom([(1 - n)/2, n mod 2 - n/2], [1 - n], -4) then a(n) = h(n-1) + h(n) for n > 3. - _Peter Luschny_, Sep 03 2019

%e 9 is in the sequence because (x, y) = (9, 23) is a solution to x^2 - 3xy + y^2 + 11 = 0.

%o (PARI) Vec(-x*(x-1)*(3*x^2+7*x+3)/((x^2-x-1)*(x^2+x-1)) + O(x^100))

%Y Cf. A001519, A005248, A055819, A237133, A218735.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Feb 04 2014