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A185728
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Array associated with squares, by antidiagonals.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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)=-1+n^2 for n>=2.
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LINKS
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FORMULA
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T(n,k)=(k-1)^2+n if n<k; T(n,n)=n^2; T(n,k)=n^2-k if n>k.
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EXAMPLE
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Northwest corner:
1...2...5...10...17
3...4...6...11...18
8...7...9...12...19
15..14..13..16...20
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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