A238339 Square number array read by ascending antidiagonals: T(1,k) = 2*k + 1, and T(n,k) = (2*n^(k+1)-n-1)/(n-1) otherwise.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 13, 7, 1, 1, 9, 25, 29, 9, 1, 1, 11, 41, 79, 61, 11, 1, 1, 13, 61, 169, 241, 125, 13, 1, 1, 15, 85, 311, 681, 727, 253, 15, 1, 1, 17, 113, 517, 1561, 2729, 2185, 509, 17, 1, 1, 19, 145, 799, 3109, 7811, 10921, 6559, 1021, 19, 1

Offset: 0

Author

Philippe Deléham, Feb 24 2014

Keywords

• easy
• nonn
• tabl

Examples

			Square array begins:
1..1...1.....1......1.......1........1........1...
1..3...5.....7......9......11.......13.......15...
1..5..13....29.....61.....125......253......509...
1..7..25....79....241.....727.....2185.....6559...
1..9..41...169....681....2729....10921....43689...
1.11..61...311...1561....7811....39061...195311...
1.13..85...517...3109...18661...111973...671845...
1.15.113...799...5601...39215...274513..1921599...
1.17.145..1169...9361...74897...599185..4793489...
1.19.181..1639..14761..132859..1195741.10761679...
1.21.221..2221..22221..222221..2222221.22222221...
		

Crossrefs

Cf. A238303.

Programs

Maple

T:= proc(n, k); if n=1 then 2*k+1 else (2*n^(k+1)-n-1)/(n-1) fi end:
seq(seq(T(n-k, k), k=0..n), n=0..10); # Georg Fischer, Oct 14 2023

Formula

T(0,k) = A000012(k) = 1;

T(1,k) = A005408(k) = 2k+1;

T(2,k) = A036563(k+2);

T(3,k) = A058481(k+1);

T(4,k) = A083584(k);

T(5,k) = A137410(k);

T(6,k) = A233325(k);

T(7,k) = A233326(k);

T(8,k) = A233328(k);

T(9,k) = A211866(k+1);

T(10,k) = A165402(k+1);

T(n,0) = A000012(n) = 1;

T(n,1) = A005408(n) = 2*n+1;

T(n,2) = A001844(n) = 2*n^2 + 2*n + 1.

Extensions

Definition amended by Georg Fischer, Oct 14 2023