A185725 Array associated with squares, by antidiagonals.

1, 2, 3, 5, 4, 6, 10, 7, 8, 11, 17, 12, 9, 13, 18, 26, 19, 14, 15, 20, 27, 37, 28, 21, 16, 22, 29, 38, 50, 39, 30, 23, 24, 31, 40, 51, 65, 52, 41, 32, 25, 33, 42, 53, 66, 82, 67, 54, 43, 34, 35, 44, 55, 68, 83, 101, 84, 69, 56, 45, 36, 46, 57, 70, 85, 102, 122, 103, 86, 71, 58, 47, 48, 59, 72, 87, 104, 123, 145, 124, 105, 88, 73, 60, 49, 61, 74, 89, 106, 125, 146, 170, 147, 126, 107, 90, 75, 62, 63, 76, 91, 108, 127, 148, 171

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.

Examples

			Northwest corner:
1...2...5...10...17
3...4...7...12...19
6...8...9...14...21
11..13..15..16...23
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A185726, A060734, A185728.

Programs

Mathematica

f[n_,k_]:=(k-1)^2+2*n-1/; n<=k;
f[n_,k_]:=(n-1)^2+2*k/; n>k;
TableForm[Table[f[n,k],{n,1,10},{k,1,15}]]
Table[f[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten

Formula

T(n,k)=(k-1)^2+2n-1 if n<=k; T(n,k)=(n-1)^2+2k if n>k.