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

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

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

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

Examples

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

Crossrefs

Cf. A185725, A060734, A185728.

Programs

Mathematica

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

Formula

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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