cp's OEIS Frontend

A261972 The first of three consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers.

%I A261972 #17 Jul 16 2025 14:09:58
%S A261972 25,361,5041,70225,978121,13623481,189750625,2642885281,36810643321,
%T A261972 512706121225,7141075053841,99462344632561,1385331749802025,
%U A261972 19295182152595801,268747218386539201,3743165875258953025,52135575035238803161,726154884618084291241
%N A261972 The first of three consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers.
%C A261972 For the first of the corresponding four consecutive positive integers, see A157088.
%H A261972 Colin Barker, <a href="/A261972/b261972.txt">Table of n, a(n) for n = 1..873</a>
%H A261972 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-15,1).
%F A261972 a(n) = 15*a(n-1)-15*a(n-2)+a(n-3) for n>3.
%F A261972 G.f.: -x*(x^2-14*x+25) / ((x-1)*(x^2-14*x+1)).
%F A261972 a(n) = (-2-(7-4*sqrt(3))^n*(-2+sqrt(3))+(2+sqrt(3))*(7+4*sqrt(3))^n)/2. - _Colin Barker_, Mar 05 2016
%e A261972 25 is in the sequence because 25^2 + 26^2 + 27^2 = 2030 = 21^2 + 22^2 + 23^2 + 24^2.
%t A261972 LinearRecurrence[{15,-15,1},{25,361,5041},20] (* _Harvey P. Dale_, Jul 16 2025 *)
%o A261972 (PARI) Vec(-x*(x^2-14*x+25)/((x-1)*(x^2-14*x+1)) + O(x^40))
%Y A261972 Cf. A157088, A261973, A261974.
%K A261972 nonn,easy
%O A261972 1,1
%A A261972 _Colin Barker_, Sep 07 2015