A257761 - OEIS

%I #20 Sep 08 2022 08:46:12

%S 92,138,4278,6532,205252,313398,9847818,15036572,472490012,721442058,

%T 22669672758,34614182212,1087671802372,1660759304118,52185576841098,

%U 79681832415452,2503820016570332,3823067196637578,120131175218534838,183427543606188292

%N Positive integers whose square is the sum of 23 consecutive squares.

%C Positive integers x in the solutions to 2*x^2-46*y^2-1012*y-7590 = 0.

%H Colin Barker, <a href="/A257761/b257761.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 (0,48,0,-1).

%F a(n) = 48*a(n-2)-a(n-4).

%F G.f.: -46*x*(x-1)*(x+2)*(2*x+1) / (x^4-48*x^2+1).

%e 92 is in the sequence because 92^2 = 8464 = 7^2+8^2+...+29^2.

%t LinearRecurrence[{0, 48, 0, -1}, {92, 138, 4278, 6532}, 30] (* _Vincenzo Librandi_, May 11 2015 *)

%o (PARI) Vec(-46*x*(x-1)*(x+2)*(2*x+1)/(x^4-48*x^2+1) + O(x^100))

%o (Magma) I:=[92,138,4278,6532]; [n le 4 select I[n] else 48*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, May 11 2015

%Y Cf. A001032, A001653, A180274, A218395, A257765, A257767, A257780, A257781, A257823-A257828.

%K nonn,easy

%O 1,1

%A _Colin Barker_, May 07 2015