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 A060736 Array of square numbers read by antidiagonals in up direction. 12
 1, 2, 4, 5, 3, 9, 10, 6, 8, 16, 17, 11, 7, 15, 25, 26, 18, 12, 14, 24, 36, 37, 27, 19, 13, 23, 35, 49, 50, 38, 28, 20, 22, 34, 48, 64, 65, 51, 39, 29, 21, 33, 47, 63, 81, 82, 66, 52, 40, 30, 32, 46, 62, 80, 100 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A simple permutation of natural numbers. a(n) is a pairing function: a function that reversibly maps Z^{+} x Z^{+} onto Z^{+}, where Z^{+} is the set of integer positive numbers. - Boris Putievskiy, Jan 09 2013 LINKS Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO]. Eric W. Weisstein, MathWorld: Pairing functions FORMULA T(n+1, k)=n*n+k, T(k, n+1)=(n+1)*(n+1)+1-k, 1 <= k <= n+1. a(n)=i^2-j+1 if i >= j, a(n)=(j-1)^2 + i if i <  j, where i=n-t*(t+1)/2, j=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Jan 09 2013 EXAMPLE 1 4 9 16 .. => a(1)= 1 2 3 8 15 .. => a(2)= 2, a(3)=4 5 6 7 14 .. => a(4)= 5, a(5)=3, a(6)=9 10 11 12 13 .. => a(7)=10, a(8)=6, a(9)=8, a(10)=16 MATHEMATICA Table[ If[n < 2*k-1, k^2 + k - n, (n-k)^2 + k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jan 09 2013 *) PROG (Python) # Boris Putievskiy, Jan 09 2013 t=int((math.sqrt(8*n-7) - 1)/ 2) i=n-t*(t+1)/2 j=(t*t+3*t+4)/2-n if i>=j:    result=i**2-j+1 else:    result=(j-1)**2+i CROSSREFS Cf. A060734. Inverse permutation: A064788, the first inverse function (numbers of rows) A194258, the second inverse function (numbers of columns) A194195. Sequence in context: A026206 A117606 A245814 * A097292 A269780 A038776 Adjacent sequences:  A060733 A060734 A060735 * A060737 A060738 A060739 KEYWORD nonn,tabl AUTHOR Frank Ellermann, Apr 23 2001 STATUS approved

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Last modified April 13 06:02 EDT 2021. Contains 342935 sequences. (Running on oeis4.)