cp's OEIS Frontend

A262140 The first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eight consecutive positive integers.

%I A262140 #9 Aug 08 2025 15:26:46
%S A262140 20,136,812,4752,27716,161560,941660,5488416,31988852,186444712,
%T A262140 1086679436,6333631920,36915112100,215157040696,1254027132092,
%U A262140 7309005751872,42600007379156,248291038523080,1447146223759340,8434586304032976,49160371600438532
%N A262140 The first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eight consecutive positive integers.
%C A262140 For the first of the corresponding eight consecutive positive integers, see A262139.
%H A262140 Colin Barker, <a href="/A262140/b262140.txt">Table of n, a(n) for n = 1..1000</a>
%H A262140 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F A262140 a(n) = 4*A076708(n+1).
%F A262140 a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.
%F A262140 G.f.: 4*x*(x-5) / ((x-1)*(x^2-6*x+1)).
%F A262140 E.g.f.: exp(x)*(exp(2*x)*(4*cosh(2*sqrt(2)*x) + 3*sqrt(2)*sinh(2*sqrt(2)*x)) - 4). - _Stefano Spezia_, Aug 08 2025
%e A262140 20 is in the sequence because 20^2 + ... + 28^2 = 5244 = 22^2 + ... + 29^2.
%o A262140 (PARI) Vec(4*x*(x-5)/((x-1)*(x^2-6*x+1)) + O(x^40))
%Y A262140 Cf. A076708, A262139.
%K A262140 nonn,easy
%O A262140 1,1
%A A262140 _Colin Barker_, Sep 12 2015