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allocatedThe first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of ten forconsecutive Colinpositive Barkerintegers.

181, 7021, 266761, 10130041, 384674941, 14607517861, 554701003921, 21064030631281, 799878462984901, 30374317562795101, 1153424188923229081, 43799744861519910121, 1663236880548833355661, 63159201715994147605141, 2398386428327228775639841

1,1

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

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

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

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

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

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

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

Cf. A262142.

allocated

nonn,easy

Colin Barker, Sep 12 2015

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