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%I #10 Sep 08 2022 08:46:12
%S 4088,23360,1582640,9047912,18642443912,106578370640,7220791811360,
%T 41281080400088,85056113063608088,486263602888235360,
%U 32944848197744794640,188344846763231651912,388068345740467131839912,2218576715650261475158640,150310804012507009263599360
%N Positive integers whose square is the sum of 73 consecutive squares.
%C Positive integers x in the solutions to 2*x^2-146*y^2-10512*y-254040 = 0.
%H Colin Barker, <a href="/A257824/b257824.txt">Table of n, a(n) for n = 1..600</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,4562498,0,0,0,-1).
%F a(n) = 4562498*a(n-4)-a(n-8).
%F G.f.: -584*x*(x-1)*(7*x^6+47*x^5+2757*x^4+18250*x^3+2757*x^2+47*x+7) / ((x^4-2136*x^2-1)*(x^4+2136*x^2-1)).
%e 4088 is in the sequence because 4088^2 = 16711744 = 442^2+443^2+...+514^2.
%t LinearRecurrence[{0, 0, 0, 4562498, 0, 0, 0, -1}, {4088, 23360, 1582640, 9047912, 18642443912, 106578370640, 7220791811360, 41281080400088}, 40] (* _Vincenzo Librandi_, May 11 2015 *)
%o (PARI) Vec(-584*x*(x-1)*(7*x^6+47*x^5+2757*x^4+18250*x^3+2757*x^2+47*x+7) / ((x^4-2136*x^2-1)*(x^4+2136*x^2-1)) + O(x^100))
%o (Magma) I:=[4088,23360,1582640,9047912,18642443912, 106578370640,7220791811360,41281080400088]; [n le 8 select I[n] else 4562498*Self(n-4)-Self(n-8): n in [1..20]]; // _Vincenzo Librandi_, May 11 2015
%Y Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823, A257825-A257828.
%K nonn,easy
%O 1,1
%A _Colin Barker_, May 10 2015
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