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

1,1

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A111774, A138591, A174069.

Sequence in context: A019552 A325728 A305662 * A045527 A353197 A306212

Adjacent sequences: A174067 A174068 A174069 * A174071 A174072 A174073

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 06 2010

Status

approved