The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A188568 Enumeration table T(n,k) by descending antidiagonals. The order of the list - if n is odd: T(n,1), T(2,n-1), T(n-2,3), ..., T(n-1,2), T(1,n); if n is even: T(1,n), T(n-1,2), T(3,n-2), ..., T(2,n-1), T(n,1). 7
 1, 2, 3, 6, 5, 4, 7, 9, 8, 10, 15, 12, 13, 14, 11, 16, 20, 18, 19, 17, 21, 28, 23, 26, 25, 24, 27, 22, 29, 35, 31, 33, 32, 34, 30, 36, 45, 38, 43, 40, 41, 42, 39, 44, 37, 46, 54, 48, 52, 50, 51, 49, 53, 47, 55 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Self-inverse 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 table read layer by layer clockwise is A194280. This table read by boustrophedonic ("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. Eric W. Weisstein, MathWorld: Pairing functions Index entries for sequences that are permutations of the natural numbers FORMULA a(n) = ((i+j-1)*(i+j-2)+((-1)^max(i,j)+1)*i-((-1)^max(i,j)-1)*j)/2, where i=n-t*(t+1)/2, j=(t*t+3*t+4)/2-n, t=floor[(-1+sqrt(8*n-7))/2]. EXAMPLE 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, 3; 6, 5, 4; 7, 9, 8, 10; 15, 12, 13, 14, 11; 16, 20, 18, 19, 17, 21; 28, 23, 26, 25, 24, 27, 22; ... Row number k contains permutation of the k numbers: { (k^2-k+2)/2, (k^2-k+2)/2 + 1, ..., (k^2+k-2)/2 + 1 }. MATHEMATICA a[n_] := Module[{t, i, j}, t = Floor[(Sqrt[8n-7]-1)/2]; i = n-t(t+1)/2; j = (t^2+3t+4)/2-n; ((i+j-1)(i+j-2) + ((-1)^Max[i, j]+1)i - ((-1)^Max[i, j]-1)j)/2]; Array[a, 55] (* Jean-François Alcover, Jan 26 2019 *) PROG (Python) t=int((math.sqrt(8*n-7) - 1)/ 2) i=n-t*(t+1)/2 j=(t*t+3*t+4)/2-n m=((i+j-1)*(i+j-2)+((-1)**max(i, j)+1)*i-((-1)**max(i, j)-1)*j)/2 CROSSREFS Cf. A056011, A056023, A057027, A064578, A194981, A194982, inverse functions A208233, A208234, A194280, A064790. Sequence in context: A089852 A122308 A122307 * A354224 A305418 A284459 Adjacent sequences: A188565 A188566 A188567 * A188569 A188570 A188571 KEYWORD nonn,tabl AUTHOR Boris Putievskiy, Dec 27 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 7 03:39 EDT 2024. Contains 375008 sequences. (Running on oeis4.)