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The first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of ten consecutive positive integers.
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%I #5 Sep 12 2015 12:43:27

%S 181,7021,266761,10130041,384674941,14607517861,554701003921,

%T 21064030631281,799878462984901,30374317562795101,1153424188923229081,

%U 43799744861519910121,1663236880548833355661,63159201715994147605141,2398386428327228775639841

%N The first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of ten consecutive positive integers.

%C For the first of the corresponding ten consecutive positive integers, see A262142.

%H Colin Barker, <a href="/A262141/b262141.txt">Table of n, a(n) for n = 1..632</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (39,-39,1).

%F a(n) = 39*a(n-1)-39*a(n-2)+a(n-3) for n>3.

%F G.f.: -x*(x^2-38*x+181) / ((x-1)*(x^2-38*x+1)).

%e 181 is in the sequence because 181^2 + ... + 189^2 = 308085 = 171^2 + ... + 180^2.

%o (PARI) Vec(-x*(x^2-38*x+181)/((x-1)*(x^2-38*x+1)) + O(x^30))

%Y Cf. A262142.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Sep 12 2015