A185728 Array associated with squares, by antidiagonals.

1, 2, 3, 5, 4, 8, 10, 6, 7, 15, 17, 11, 9, 14, 24, 26, 18, 12, 13, 23, 35, 37, 27, 19, 16, 22, 34, 48, 50, 38, 28, 20, 21, 33, 47, 63, 65, 51, 39, 29, 25, 32, 46, 62, 80, 82, 66, 52, 40, 30, 31, 45, 61, 79, 99, 101, 83, 67, 53, 41, 36, 44, 60, 78, 98, 120, 122, 102, 84, 68, 54, 42, 43, 59, 77, 97, 119, 143, 145, 123, 103, 85, 69, 55, 49, 58, 76, 96, 118, 142, 168, 170, 146, 124, 104, 86, 70, 56, 57, 75, 95, 117, 141, 167, 195

Offset: 1

Author

Clark Kimberling, Feb 01 2011

Keywords

• nonn
• tabl

Comments

Every positive integer occurs exactly once; hence, as a sequence, A185725 is a permutation of the positive integers. The square with corners T(0,0)=1 and T(n,n)=n^2 is occupied by the numbers 1,2,...,n^2.

T(1,k)=(k-1)^2+1 (A002522)

T(n,1)=-1+n^2 for n>=2.

Examples

			Northwest corner:
1...2...5...10...17
3...4...6...11...18
8...7...9...12...19
15..14..13..16...20
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A185725, A185726, A060734.

Programs

Mathematica

f[n_,k_]:=(k-1)^2+n/; k>n;
f[n_,n_]:=n^2; f[n_,k_]:=n^2-k/; k
				

Formula

T(n,k)=(k-1)^2+n if nk.