A121490 Rectangular array T by antidiagonals: T(n,k) = [y+1]^2-y^2, where y=n*sqrt(k) and [ ] denotes the floor function.

3, 2, 5, 1, 1, 7, 5, 4, 7, 9, 4, 9, 9, 4, 11, 3, 5, 13, 1, 14, 13, 2, 1, 4, 17, 6, 9, 15, 1, 8, 10, 1, 21, 13, 2, 17, 7, 4, 1, 4, 19, 25, 22, 16, 19, 6, 13, 9, 9, 19, 16, 29, 4, 7, 21, 5, 9, 19, 16, 21, 9, 11, 33, 13, 25, 23, 4, 5, 10, 25, 25, 4, 30, 4, 37, 24, 14, 25, 3, 1, 1, 9, 31, 1, 18, 16

Offset: 1

Author

Clark Kimberling, Aug 02 2006

Keywords

• nonn
• tabl

Comments

(Row 1)=A080883; (Column 1)=A005408 except for initial term; (Column 2)=A087059; (Column 3)=A120865; (Column 4)=A016813 except for initial term; (Column 5)=A120867; Columns 1,4,9,16,25,... are arithmetic sequences; (Main diagonal)=A121489.

Examples

			Northwest corner:
3 2 1 5 4
5 1 4 9 5
7 7 9 13 4
9 4 1 17 1
		

Formula

T(n,k) = [y+1]^2-y^2