A185726 Array associated with squares, by antidiagonals.

1, 3, 4, 8, 10, 10, 18, 22, 24, 21, 35, 44, 45, 48, 39, 61, 80, 81, 84, 86, 66, 98, 134, 138, 136, 144, 142, 104, 148, 210, 222, 216, 220, 231, 220, 155, 213, 312, 339, 332, 325, 340, 351, 324, 221, 295, 444, 495, 492, 475, 480, 504, 510, 458, 304, 396, 610, 696, 704, 680, 666, 690, 720, 714, 626, 406, 518, 814, 948, 976, 950, 918, 924, 965, 996, 969, 832, 529, 663, 1060, 1257, 1316, 1295, 1248, 1225, 1260, 1315, 1340, 1281, 1080, 675, 833, 1352, 1629, 1732, 1725

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(n,1)=n^2 (A000290)

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

T(1,k)=k^2-1 (A132411).

Links

Table of n, a(n) for n=1..96.

Formula

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

Example

Northwest corner:
1...3...8...15...24
4...2...6...13...22
9...7...5...11...20
16..14..12..10...18

Mathematica

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

Crossrefs

Cf. A185725, A060734, A185728.

Sequence in context: A253606 A258640 A345223 * A152520 A239976 A191193

Adjacent sequences: A185723 A185724 A185725 * A185727 A185728 A185729

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 01 2011

Status

approved