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

30, 54, 55, 86, 90, 91, 126, 135, 139, 140, 174, 190, 199, 203, 204, 230, 255, 271, 280, 284, 285, 294, 330, 355, 366, 371, 380, 384, 385, 415, 446, 451, 476, 492, 501, 505, 506, 510, 534, 559, 595, 615, 620, 630, 636, 645, 649, 650, 679, 728, 730, 734, 764

Offset

1,1

Comments

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

Links

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

Example

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, ...

Maple

N:= 1000: # to get all terms <= N
Res:= NULL:
for m from 4 while m*(m+1)*(2*m+1)/6 <= N do
   for k from 1 do
       v:= m*(6*k^2 + 6*k*m + 2*m^2 - 6*k - 3*m + 1)/6;
       if v > N then break fi;
       Res:= Res, v;
od od:
sort(convert({Res}, list));  Robert Israel, May 06 2019

Mathematica

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]

Crossrefs

Cf. A111774, A138591, A174069, A174070, A307937.

Sequence in context: A043172 A043952 A304047 * A006315 A027578 A189712

Adjacent sequences: A174068 A174069 A174070 * A174072 A174073 A174074

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 06 2010

Extensions

Edited by Robert Israel, May 06 2019

Status

approved