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Square array T(n, k) read by antidiagonals upwards, n >= 0 and k >= 0: the point with coordinates X=k and Y=n is the T(n, k)-th term of the first type of Wunderlich curve.
1

%I #6 Jan 15 2019 18:44:22

%S 1,2,6,3,5,7,48,4,8,16,49,47,9,15,17,54,50,46,10,14,18,55,53,51,45,11,

%T 13,19,56,60,52,44,40,12,20,24,57,59,61,43,41,39,21,23,25,462,58,62,

%U 70,42,38,30,22,26,106,463,461,63,69,71,37,31,29,27,105,107

%N Square array T(n, k) read by antidiagonals upwards, n >= 0 and k >= 0: the point with coordinates X=k and Y=n is the T(n, k)-th term of the first type of Wunderlich curve.

%C Each natural numbers appears once in the sequence.

%H Robert Dickau, <a href="http://robertdickau.com/wunderlich.html">Wunderlich Curves</a>

%H Wolfram Demonstrations Project, <a href="https://demonstrations.wolfram.com/WunderlichCurves/">Wunderlich Curves</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F T(A323259(n), A323258(n)) = n.

%e Array T(n, k) begins:

%e n\k| 0 1 2 3 4 5 6 7 8

%e ---+------------------------------------

%e 0 | 1 6---7 16--17--18--19 24--25

%e | | | | | | | |

%e 1 | 2 5 8 15--14--13 20 23 26

%e | | | | | | | |

%e 2 | 3---4 9--10--11--12 21--22 27

%e | |

%e 3 | 48--47--46--45 40--39 30--29--28

%e | | | | | |

%e 4 | 49--50--51 44 41 38 31--32--33

%e | | | | | |

%e 5 | 54--53--52 43--42 37--36--35--34

%e | |

%e 6 | 55 60--61 70--71--72--73 78--79

%e | | | | | | | |

%e 7 | 56 59 62 69--68--67 74 77 80

%e | | | | | | | |

%e 8 | 57--58 63--64--65--66 75--76 81

%Y See A163334 for a similar sequence.

%Y Cf. A323258, A323259.

%K nonn,tabl

%O 0,2

%A _Rémy Sigrist_, Jan 11 2019