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A185725
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Array associated with squares, by antidiagonals.
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6
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1, 2, 3, 5, 4, 6, 10, 7, 8, 11, 17, 12, 9, 13, 18, 26, 19, 14, 15, 20, 27, 37, 28, 21, 16, 22, 29, 38, 50, 39, 30, 23, 24, 31, 40, 51, 65, 52, 41, 32, 25, 33, 42, 53, 66, 82, 67, 54, 43, 34, 35, 44, 55, 68, 83, 101, 84, 69, 56, 45, 36, 46, 57, 70, 85, 102, 122, 103, 86, 71, 58, 47, 48, 59, 72, 87, 104, 123, 145, 124, 105, 88, 73, 60, 49, 61, 74, 89, 106, 125, 146, 170, 147, 126, 107, 90, 75, 62, 63, 76, 91, 108, 127, 148, 171
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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.
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LINKS
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FORMULA
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T(n,k)=(k-1)^2+2n-1 if n<=k; T(n,k)=(n-1)^2+2k if n>k.
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EXAMPLE
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Northwest corner:
1...2...5...10...17
3...4...7...12...19
6...8...9...14...21
11..13..15..16...23
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MATHEMATICA
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f[n_, k_]:=(k-1)^2+2*n-1/; n<=k;
f[n_, k_]:=(n-1)^2+2*k/; 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
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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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