A181524 Table read by rows in which n-th row gives the smallest solution (a,b,c,d) to the partition (4n+1)^2 = a^2 + b^2 + c^2 + d^2 with 0 < a < b < c < d.

2, 4, 5, 6, 1, 2, 8, 10, 2, 4, 10, 13, 1, 2, 6, 20, 2, 3, 6, 24, 1, 8, 10, 26, 2, 3, 20, 26, 1, 4, 14, 34, 1, 4, 8, 40, 1, 2, 16, 42, 1, 4, 28, 40, 1, 2, 10, 52, 1, 4, 36, 44, 1, 2, 40, 46, 1, 8, 32, 56, 1, 2, 20, 66, 1, 16, 44, 56, 1, 2, 32, 70, 1, 4, 12, 80, 1, 2, 38, 76, 2, 4, 26, 85, 1, 2, 30, 88, 1, 8, 40, 88, 1, 2, 14, 100, 1, 8, 12, 104, 1, 2, 74, 80, 1, 4, 44, 104, 1, 4, 26, 114, 1, 4, 68, 100, 1, 6, 72, 102, 1, 32, 80, 96, 1, 2, 28, 130, 1, 4, 16, 136, 1, 2, 74, 120, 1, 4, 68, 128, 1, 10, 14, 148, 2, 3, 70, 136, 1, 2, 88, 130, 1, 8, 16, 160

Offset: 2

Author

Pedro Fernandez (fourier07(AT)gmail.com), Oct 26 2010

Keywords

• nonn
• tabf

Comments

Solutions to the Diophantine partition of (4n+1)^2 into 4 distinct nonzero squares are counted in A175958.

The table contains four numbers a,b,c,d in row n illustrating one particular solution, minimizing a, if there are two solutions with the same a minimizing b etc.

Examples

			The table starts in row n=2 as
  2,  4,  5,  6; # 2^2 + 4^2 +  5^2 +  6^2 = (4*2+1)^2
  1,  2,  8, 10; # 1^2 + 2^2 +  8^2 + 10^2 = (4*3+1)^2
  2,  4, 10, 13; # 2^2 + 4^2 + 10^2 + 13^2 = (4*4+1)^2
		

Extensions

Replaced the 4 terms with a generic definition; connected to A175958 - R. J. Mathar, Nov 17 2010