cp's OEIS Frontend

A262139 The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.

%I A262139 #12 Apr 19 2016 09:36:51
%S A262139 22,145,862,5041,29398,171361,998782,5821345,33929302,197754481,
%T A262139 1152597598,6717831121,39154389142,228208503745,1330096633342,
%U A262139 7752371296321,45184131144598,263352415571281,1534930362283102,8946229758127345,52142448186480982
%N A262139 The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.
%C A262139 For the first of the corresponding nine consecutive positive integers, see A262140.
%H A262139 Colin Barker, <a href="/A262139/b262139.txt">Table of n, a(n) for n = 1..1000</a>
%H A262139 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F A262139 a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.
%F A262139 G.f.: -x*(x^2-9*x+22) / ((x-1)*(x^2-6*x+1)).
%F A262139 a(n) = (-14+3*(3-2*sqrt(2))^(1+n)+3*(3+2*sqrt(2))^(1+n))/4. - _Colin Barker_, Mar 05 2016
%e A262139 22 is in the sequence because 22^2 + ... + 29^2 = 5244 = 20^2 + ... + 28^2.
%t A262139 LinearRecurrence[{7,-7,1},{22,145,862},30] (* _Harvey P. Dale_, Apr 19 2016 *)
%o A262139 (PARI) Vec(-x*(x^2-9*x+22)/((x-1)*(x^2-6*x+1)) + O(x^40))
%Y A262139 Cf. A262140.
%K A262139 nonn,easy
%O A262139 1,1
%A A262139 _Colin Barker_, Sep 12 2015