A245022 Integers with precisely three partitions into sums of four squares of nonnegative numbers.

18, 25, 26, 27, 28, 33, 37, 38, 41, 43, 51, 53, 55, 59, 60, 62, 72, 79, 92, 95, 104, 112, 152, 240, 248, 288, 368, 416, 448, 608, 960, 992, 1152, 1472, 1664, 1792, 2432, 3840, 3968, 4608, 5888, 6656, 7168, 9728, 15360, 15872, 18432, 23552, 26624, 28672

Offset: 1

Author

Reinhard Zumkeller, Jul 13 2014

Keywords

• nonn

Comments

A002635(a(n)) = 3.

Examples

			a(1) = 18 = 16 + 1 + 1 + 0 = 9 + 9 + 0 + 0 = 9 + 4 + 4 + 1;
a(2) = 25 = 25 + 0 + 0 + 0 = 16 + 9 + 0 + 0 = 16 + 4 + 4 + 1;
a(3) = 26 = 25 + 1 + 0 + 0 = 16 + 9 + 1 + 0 = 9 + 9 + 4 + 4;
a(4) = 27 = 25 + 1 + 1 + 0 = 16 + 9 + 1 + 1 = 9 + 9 + 9 + 0;
a(5) = 28 = 25 + 1 + 1 + 1 = 16 + 4 + 4 + 4 = 9 + 9 + 9 + 1;
a(6) = 33 = 25 + 4 + 4 + 0 = 16 + 16 + 1 + 0 = 16 + 9 + 4 + 4;
a(7) = 37 = 36 + 1 + 0 + 0 = 25 + 4 + 4 + 4 = 16 + 16 + 4 + 1;
a(8) = 38 = 36 + 1 + 1 + 0 = 25 + 9 + 4 + 0 = 16 + 9 + 9 + 4;
a(9) = 41 = 36 + 4 + 1 + 0 = 25 + 16 + 0 + 0 = 16 + 16 + 9 + 0;
a(10) = 43 = 25 + 16 + 1 + 1 = 25 + 9 + 9 + 0 = 16 + 9 + 9 + 9;
a(11) = 51 = 49 + 1 + 1 + 0 = 25 + 25 + 1 + 0 = 25 + 16 + 9 + 1;
a(12) = 53 = 49 + 4 + 0 + 0 = 36 + 16 + 1 + 0 = 36 + 9 + 4 + 4.
		

Links

• Robert Price, Table of n, a(n) for n = 1..55
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A002635, A006431, A180149.

Programs

Haskell

a245022 n = a245022_list !! (n-1)
a245022_list = filter ((== 3) . a002635) [0..]

Mathematica

Select[ Range@ 30000, Length@PowersRepresentations[#, 4, 2] == 3 &] (* Robert G. Wilson v, Oct 27 2017 *)

Extensions

a(44)-a(50) from Robert Price, Oct 26 2017