A080818 Triangle read by rows in which the n-th row contains n distinct numbers whose sum is the smallest square.

1, 1, 3, 1, 2, 6, 1, 2, 3, 10, 1, 2, 3, 4, 6, 1, 2, 3, 4, 5, 10, 1, 2, 3, 4, 5, 6, 15, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 22, 1, 2, 3, 4, 5, 6, 7, 8

Offset: 1

Author

Amarnath Murthy, Mar 21 2003

Keywords

• nonn
• tabl

Comments

If n(n+1)/2 is a square triangular number then the n-th row contains first n natural numbers (e.g., the 8th row).

Examples

			1; 1,3; 1,2,6; 1,2,3,10; 1,2,3,4,6; 1,2,3,4,5,10; 1,2,3,4,5,6,15; 1,2,3,4,5,6,...
		

Crossrefs

Cf. A080817, A080819, A080820.

Programs

Maple

seq(op([seq(i,i=1..n-1),(ceil(sqrt(n*(n+1)/2)))^2 - n*(n-1)/2]),n=1..15); # C. Ronaldo

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004