A262139 - OEIS

%I #12 Apr 19 2016 09:36:51

%S 22,145,862,5041,29398,171361,998782,5821345,33929302,197754481,

%T 1152597598,6717831121,39154389142,228208503745,1330096633342,

%U 7752371296321,45184131144598,263352415571281,1534930362283102,8946229758127345,52142448186480982

%N 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 For the first of the corresponding nine consecutive positive integers, see A262140.

%H Colin Barker, <a href="/A262139/b262139.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).

%F a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.

%F G.f.: -x*(x^2-9*x+22) / ((x-1)*(x^2-6*x+1)).

%F a(n) = (-14+3*(3-2*sqrt(2))^(1+n)+3*(3+2*sqrt(2))^(1+n))/4. - _Colin Barker_, Mar 05 2016

%e 22 is in the sequence because 22^2 + ... + 29^2 = 5244 = 20^2 + ... + 28^2.

%t LinearRecurrence[{7,-7,1},{22,145,862},30] (* _Harvey P. Dale_, Apr 19 2016 *)

%o (PARI) Vec(-x*(x^2-9*x+22)/((x-1)*(x^2-6*x+1)) + O(x^40))

%Y Cf. A262140.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Sep 12 2015