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 A060734 Natural numbers written as a square array ending in last row from left to right and rightmost column from bottom to top are read by antidiagonals downwards. 15
 1, 4, 2, 9, 3, 5, 16, 8, 6, 10, 25, 15, 7, 11, 17, 36, 24, 14, 12, 18, 26, 49, 35, 23, 13, 19, 27, 37, 64, 48, 34, 22, 20, 28, 38, 50, 81, 63, 47, 33, 21, 29, 39, 51, 65, 100, 80, 62, 46, 32, 30, 40, 52, 66, 82, 121, 99, 79, 61, 45, 31, 41, 53, 67, 83, 101 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A simple permutation of natural numbers. Parity of the sequence is given by A057211 (n-th run has length n). - Jeremy Gardiner, Dec 26 2008 The square with corners T(1,1)=1 and T(n,n)=n^2-n+1 is occupied by the numbers 1,2,...,n^2. - Clark Kimberling, Feb 01 2011 a(n) is pairing function - function that reversibly maps Z^{+} x Z^{+} onto Z^{+}, where Z^{+} - the set of integer positive numbers. - Boris Putievskiy, Dec 17 2012 LINKS Alois P. Heinz, Rows n = 1..141 of triangle, flattened Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012. Eric W. Weisstein, MathWorld: Pairing functions FORMULA T(n,k) = (n-1)^2+k, T(k, n)=n^2+1-k, 1 <= k <= n. From Clark Kimberling, Feb 01 2011: (Start) T(1,k) = k^2 (A000290). T(n,n) = n^2-n+1 (A002061). T(n,1) = (n-1)^2+1 (A002522). (End) EXAMPLE Northwest corner: .1  4  9 16 ..  => a(1) =  1 .2  3  8 15 ..  => a(2) =  4, a(3) = 2 .5  6  7 14 ..  => a(4) =  9, a(5) = 3, a(6) = 5 10 11 12 13 ..  => a(7) = 16, a(8) = 8, a(9) = 6, a(10)=10 MAPLE T:= (n, k)-> `if`(n<=k, k^2-n+1, (n-1)^2+k): seq(seq(T(n, d-n), n=1..d-1), d=2..15); MATHEMATICA f[n_, k_]:=k^2-n+1/; k>=n; f[n_, k_]:=(n-1)^2+k/; k

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)