A174070 Numbers that can be written as a sum of at least 3 consecutive squares.

14, 29, 30, 50, 54, 55, 77, 86, 90, 91, 110, 126, 135, 139, 140, 149, 174, 190, 194, 199, 203, 204, 230, 245, 255, 271, 280, 284, 285, 294, 302, 330, 355, 365, 366, 371, 380, 384, 385, 415, 434, 446, 451, 476, 492, 501, 505, 506, 509, 510, 534, 559, 590, 595

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 06 2010

Keywords

• nonn

Comments

Numbers of the form (a(a+1)(2a+1)-b(b+1)(2b+1))/6 where a >= b+3 and b >= 0. - Robert Israel, Jul 18 2017

Examples

			14 = 1^2 + 2^2 + 3^2, 29 = 2^2 + 3^2 + 4^2.
30 = 1^2 + 2^2 + 3^2 + 4^2, 50 = 3^2 + 4^2 + 5^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111774, A138591, A174069.

Programs

Maple

N:= 1000: # to get all terms <= N
R:= [seq(b*(b+1)*(2*b+1)/6, b=0..ceil(sqrt(N/3)))]:
sort(convert(select(`<=`, {seq(seq(R[i]-R[j],j=1..i-3),i=1..nops(R))},N),list)); # Robert Israel, Jul 18 2017

Mathematica

max=50^2;lst={};Do[z=n^2+(n+1)^2;Do[z+=(n+x)^2;If[z>max,Break[]];AppendTo[lst,z],{x,2,max/2}],{n,max/2}];Union[lst]
(* Second program: *)
Function[s, Function[t, Union@ Flatten@ Map[TakeWhile[#, # < t[[1, -1]] &] &, t]]@ Map[Total /@ Partition[s, #, 1] &, Range[3, Length@ s]]][Range[16]^2] (* Michael De Vlieger, Jul 18 2017 *)
Module[{nn=30,sq},sq=Range[nn]^2;Take[Union[Flatten[Table[Total/@ Partition[ sq,n,1],{n,3,nn-2}]]],2nn]] (* Harvey P. Dale, Nov 16 2017 *)