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A174071 Numbers that can be written as a sum of at least 4 consecutive positive squares.

%I A174071 #7 May 06 2019 20:54:49
%S A174071 30,54,55,86,90,91,126,135,139,140,174,190,199,203,204,230,255,271,
%T A174071 280,284,285,294,330,355,366,371,380,384,385,415,446,451,476,492,501,
%U A174071 505,506,510,534,559,595,615,620,630,636,645,649,650,679,728,730,734,764
%N A174071 Numbers that can be written as a sum of at least 4 consecutive positive squares.
%C A174071 Numbers of the form  m*(6*k^2 + 6*k*m + 2*m^2 - 6*k - 3*m + 1)/6 for some m>=4 and k>=1. - _Robert Israel_, May 06 2019
%H A174071 Robert Israel, <a href="/A174071/b174071.txt">Table of n, a(n) for n = 1..10000</a>
%e A174071 30=1^2+2^2+3^2+4^2, 54=2^2+3^2+4^2+5^2, 55=1^2+2^2+3^2+4^2+5^2, ...
%p A174071 N:= 1000: # to get all terms <= N
%p A174071 Res:= NULL:
%p A174071 for m from 4 while m*(m+1)*(2*m+1)/6 <= N do
%p A174071    for k from 1 do
%p A174071        v:= m*(6*k^2 + 6*k*m + 2*m^2 - 6*k - 3*m + 1)/6;
%p A174071        if v > N then break fi;
%p A174071        Res:= Res, v;
%p A174071 od od:
%p A174071 sort(convert({Res},list));  _Robert Israel_, May 06 2019
%t A174071 max=60^2;lst={};Do[z=n^2+(n+1)^2+(n+2)^2;Do[z+=(n+x)^2;If[z>max,Break[]];AppendTo[lst,z],{x,3,Sqrt[max]/2}],{n,Sqrt[max]/2}];Union[lst]
%Y A174071 Cf. A111774, A138591, A174069, A174070, A307937.
%K A174071 nonn
%O A174071 1,1
%A A174071 _Vladimir Joseph Stephan Orlovsky_, Mar 06 2010
%E A174071 Edited by _Robert Israel_, May 06 2019