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A257765 Positive integers whose square is the sum of 26 consecutive squares.

%I A257765 #21 Mar 10 2024 16:13:32
%S A257765 195,1599,2379,19695,163059,242619,2008695,16630419,24744759,
%T A257765 204867195,1696139679,2523722799,20894445195,172989616839,
%U A257765 257394980739,2131028542695,17643244777899,26251764312579,217344016909695,1799437977728859,2677422564902319
%N A257765 Positive integers whose square is the sum of 26 consecutive squares.
%C A257765 Positive integers x in the solutions to 2*x^2-52*y^2-1300*y-11050 = 0.
%H A257765 Colin Barker, <a href="/A257765/b257765.txt">Table of n, a(n) for n = 1..1000</a>
%H A257765 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,102,0,0,-1).
%F A257765 a(n) = 102*a(n-3)-a(n-6).
%F A257765 G.f.: -39*x*(x^5+x^4+5*x^3-61*x^2-41*x-5) / (x^6-102*x^3+1).
%e A257765 195 is in the sequence because 195^2 = 38025 = 25^2+26^2+...+50^2.
%t A257765 LinearRecurrence[{0, 0, 102, 0, 0, -1}, {195, 1599, 2379, 19695, 163059, 242619}, 30] (* _Vincenzo Librandi_, May 11 2015 *)
%t A257765 Select[Sqrt[#]&/@Total/@Partition[Range[10^6]^2,26,1],IntegerQ] (* The program generates the first 7 terms of the sequence. *) (* _Harvey P. Dale_, Mar 10 2024 *)
%o A257765 (PARI) Vec(-39*x*(x^5+x^4+5*x^3-61*x^2-41*x-5) / (x^6-102*x^3+1) + O(x^100))
%o A257765 (Magma) I:=[195,1599,2379,19695,163059,242619 ]; [n le 6 select I[n] else 102*Self(n-3)-Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, May 11 2015
%Y A257765 Cf. A001032, A001653, A180274, A218395, A257761, A257767, A257780, A257781, A257823-A257828.
%K A257765 nonn,easy
%O A257765 1,1
%A A257765 _Colin Barker_, May 07 2015