cp's OEIS Frontend

A261974 The first of eleven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of three consecutive positive integers.

%I A261974 #12 Jul 02 2016 12:57:01
%S A261974 67,3307,152275,7001563,321919843,14801311435,680538406387,
%T A261974 31289965382587,1438657869192835,66146972017488043,
%U A261974 3041322054935257363,139834667555004350875,6429353385475264883107,295610421064307180272267,13591650015572655027641395
%N A261974 The first of eleven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of three consecutive positive integers.
%C A261974 For the first of the corresponding three consecutive positive integers, see A261973.
%H A261974 Colin Barker, <a href="/A261974/b261974.txt">Table of n, a(n) for n = 1..601</a>
%H A261974 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (47,-47,1).
%F A261974 a(n) = 47*a(n-1)-47*a(n-2)+a(n-3) for n>3.
%F A261974 G.f.: x*(5*x^2-158*x-67) / ((x-1)*(x^2-46*x+1)).
%F A261974 a(n) = -5+3*sqrt(3/11)*(23+4*sqrt(33))^(-n)*(-1+(23+4*sqrt(33))^(2*n)). - _Colin Barker_, Mar 03 2016
%e A261974 67 is in the sequence because 67^2 + ... + 77^2 = 57134 = 137^2 + 138^2 + 139^2.
%t A261974 LinearRecurrence[{47,-47,1},{67,3307,152275},20] (* _Harvey P. Dale_, Jul 02 2016 *)
%o A261974 (PARI) Vec(x*(5*x^2-158*x-67)/((x-1)*(x^2-46*x+1)) + O(x^40))
%Y A261974 Cf. A157088, A261972, A261973.
%K A261974 nonn,easy
%O A261974 1,1
%A A261974 _Colin Barker_, Sep 07 2015