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A261933 The first of two consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seventeen consecutive positive integers.

%I A261933 #7 Oct 17 2015 13:48:23
%S A261933 40,91,2743,6364,192004,445423,13437571,31173280,940438000,2181684211,
%T A261933 65817222463,152686721524,4606265134444,10685888822503,
%U A261933 322372742188651,747859530853720,22561485688071160,52339481270937931,1578981625422792583,3663015829434801484
%N A261933 The first of two consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seventeen consecutive positive integers.
%C A261933 For the first of the corresponding seventeen consecutive positive integers, see A261935.
%H A261933 Colin Barker, <a href="/A261933/b261933.txt">Table of n, a(n) for n = 1..1000</a>
%H A261933 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,70,-70,-1,1).
%F A261933 G.f.: -x*(40*x^4+51*x^3-148*x^2+51*x+40) / ((x-1)*(x^4-70*x^2+1)).
%e A261933 40 is in the sequence because 40^2 + 41^2 = 5^2 + 6^2 + ... + 21^2.
%t A261933 LinearRecurrence[{1,70,-70,-1,1},{40,91,2743,6364,192004},20] (* _Harvey P. Dale_, Oct 17 2015 *)
%o A261933 (PARI) Vec(-x*(40*x^4+51*x^3-148*x^2+51*x+40)/((x-1)*(x^4-70*x^2+1)) + O(x^40))
%Y A261933 Cf. A001652, A031138, A261932, A261934, A261935.
%K A261933 nonn,easy
%O A261933 1,1
%A A261933 _Colin Barker_, Sep 06 2015