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A262017 The first of five consecutive positive integers the sum of the squares of which is equal to the sum of the squares of six consecutive positive integers.

%I A262017 #9 Sep 09 2015 06:48:03
%S A262017 61,1381,30361,666601,14634901,321301261,7053992881,154866542161,
%T A262017 3400009934701,74645352021301,1638797734533961,35978904807725881,
%U A262017 789897108035435461,17341757471971854301,380728767275345359201,8358691122585626048161,183510475929608427700381
%N A262017 The first of five consecutive positive integers the sum of the squares of which is equal to the sum of the squares of six consecutive positive integers.
%C A262017 For the first of the corresponding six consecutive positive integers, see A157096.
%H A262017 Colin Barker, <a href="/A262017/b262017.txt">Table of n, a(n) for n = 1..744</a>
%H A262017 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (23,-23,1).
%F A262017 a(n) = 23*a(n-1)-23*a(n-2)+a(n-3) for n>3.
%F A262017 G.f.: -x*(x^2-22*x+61) / ((x-1)*(x^2-22*x+1)).
%e A262017 61 is in the sequence because 61^2 + ... + 65^2 = 19855 = 55^2 + ... + 60^2.
%o A262017 (PARI) Vec(-x*(x^2-22*x+61)/((x-1)*(x^2-22*x+1)) + O(x^40))
%Y A262017 Cf. A157096, A262018, A262019.
%Y A262017 Cf. A027578, A027865.
%K A262017 nonn,easy
%O A262017 1,1
%A A262017 _Colin Barker_, Sep 08 2015