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 A194280 Inverse permutation to A081344. 7
 1, 2, 5, 3, 6, 9, 13, 8, 4, 7, 12, 18, 25, 19, 14, 10, 15, 20, 26, 33, 41, 32, 24, 17, 11, 16, 23, 31, 40, 50, 61, 51, 42, 34, 27, 21, 28, 35, 43, 52, 62, 73, 85, 72, 60, 49, 39, 30, 22, 29, 38, 48, 59, 71, 84, 98, 113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Permutation of the 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. Call a "layer" a pair of sides of square from T(1,n) to T(n,n) and from T(n,n) to T(n,1). This sequence is A188568 as table read layer by layer clockwise. The same table A188568 read  by boustrophedon ("ox-plowing") method - layer clockwise, layer counterclockwise and so on - is A064790. - Boris Putievskiy, Mar 14 2013 LINKS Boris Putievskiy, Rows n = 1..140 of triangle, flattened Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012. FORMULA a(n) = (i+j-1)*(i+j-2)/2+j, where i = mod(t;2)*min{t; n - (t - 1)^2} + mod(t + 1; 2)*min{t; t^2 - n + 1} j = mod(t;2)*min{t; t^2 - n + 1} + mod(t + 1; 2)*min{t; n - (t - 1)^2}, t = int(math.sqrt(n-1))+1. EXAMPLE From Boris Putievskiy, Mar 14 2013: (Start) The start of the sequence as table:   1....2...6...7..15..16..28...   3....5...9..12..20..23..35...   4....8..13..18..26..31..43...   10..14..19..25..33..40..52...   11..17..24..32..41..50..62...   21..27..34..42..51..61..73...   22..30..39..49..60..72..85...   ... The start of the sequence as triangular array read by rows:   1;   2,5,3;   6,9,13,8,4;   7,12,18,25,19,14,10;   15,20,26,33,41,32,24,17,11;   16,23,31,40,50,61,51,42,34,27,21;   28,35,43,52,62,73,85,72,60,49,39,30,22;   ... Row number r contains 2*r-1 numbers. (End) PROG (Python) t=int(math.sqrt(n-1))+1 i=(t % 2)*min(t, n-(t-1)**2) + ((t+1) % 2)*min(t, t**2-n+1) j=(t % 2)*min(t, t**2-n+1) + ((t+1) % 2)*min(t, n-(t-1)**2) m=(i+j-1)*(i+j-2)/2+j CROSSREFS Cf. A081344, A064790, A188568. Sequence in context: A335499 A239970 A111202 * A163362 A243061 A242911 Adjacent sequences:  A194277 A194278 A194279 * A194281 A194282 A194283 KEYWORD nonn AUTHOR Boris Putievskiy, Dec 23 2012 STATUS approved

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Last modified April 13 07:25 EDT 2021. Contains 342935 sequences. (Running on oeis4.)