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

1,2

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.

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A185725, A185726, A060734.

Sequence in context: A183209 A046708 A338251 * A285492 A272090 A120255

Adjacent sequences: A185725 A185726 A185727 * A185729 A185730 A185731

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 01 2011

Status

approved