%I #9 Sep 08 2022 08:46:13
%S 26,598,90688,1891916,285495236,5955760408,898738921678,
%T 18748731881906,2829229839956546,59021002008489118,
%U 8906414637444294568,185798095573991870996,28037390449444799352956,584892345845924401415728,88261696228437590918820358
%N The first of seven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of thirteen consecutive positive integers.
%C For the first of the corresponding thirteen consecutive positive integers, see A262077.
%H Colin Barker, <a href="/A262076/b262076.txt">Table of n, a(n) for n = 1..572</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,3148,-3148,-1,1).
%F a(n) = a(n-1)+3148*a(n-2)-3148*a(n-3)-a(n-4)+a(n-5) for n>5.
%F G.f.: -26*x*(x^4+22*x^3+317*x^2+22*x+1) / ((x-1)*(x^4-3148*x^2+1)).
%e 26 is in the sequence because 26^2 + ... + 32^2 = 5915 = 15^2 + ... + 27^2.
%t LinearRecurrence[{1, 3148, -3148, -1, 1}, {26, 598, 90688, 1891916, 285495236}, 20] (* _Vincenzo Librandi_, Sep 11 2015 *)
%o (PARI) Vec(-26*x*(x^4+22*x^3+317*x^2+22*x+1)/((x-1)*(x^4-3148*x^2+1)) + O(x^20))
%o (Magma) I:=[26,598,90688,1891916,285495236]; [n le 5 select I[n] else Self(n-1)+3148*Self(n-2)-3148*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // _Vincenzo Librandi_, Sep 11 2015
%Y Cf. A262074, A262075, A262077.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Sep 10 2015