cp's OEIS Frontend

A257780 Positive integers whose square is the sum of 47 consecutive squares.

%I A257780 #13 Sep 08 2022 08:46:12
%S A257780 3854,5170,369890,496226,35505586,47632526,3408166366,4572226270,
%T A257780 327148465550,438886089394,31402844526434,42128492355554,
%U A257780 3014345926072114,4043896380043790,289345806058396510,388171923991848286,27774183035679992846,37260460806837391666
%N A257780 Positive integers whose square is the sum of 47 consecutive squares.
%C A257780 Positive integers x in the solutions to 2*x^2-94*y^2-4324*y-67022 = 0.
%H A257780 Colin Barker, <a href="/A257780/b257780.txt">Table of n, a(n) for n = 1..1000</a>
%H A257780 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,96,0,-1).
%F A257780 a(n) = 96*a(n-2)-a(n-4).
%F A257780 G.f.: -94*x*(x^3+x^2-55*x-41) / (x^4-96*x^2+1).
%e A257780 3854 is in the sequence because 3854^2 = 14853316 = 539^2+540^2+...+585^2.
%t A257780 LinearRecurrence[{0, 96, 0, -1}, {3854, 5170, 369890, 496226}, 50] (* _Vincenzo Librandi_, May 11 2015 *)
%o A257780 (PARI) Vec(-94*x*(x^3+x^2-55*x-41) / (x^4-96*x^2+1) + O(x^100))
%o A257780 (Magma) I:=[3854,5170,369890,496226 ]; [n le 4 select I[n] else 96*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, May 11 2015
%Y A257780 Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257781, A257823-A257828.
%K A257780 nonn,easy
%O A257780 1,1
%A A257780 _Colin Barker_, May 08 2015