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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

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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