%I #12 Jul 02 2016 22:53:13
%S 1,3,2,5,6,4,9,8,10,7,13,14,12,15,11,19,18,20,17,21,16,25,26,24,27,23,
%T 28,22,33,32,34,31,35,30,36,29,41,42,40,43,39,44,38,45,37,51,50,52,49,
%U 53,48,54,47,55,46,61,62,60,63,59,64,58,65,57,66,56
%N Triangle T read by rows: row n consists of the numbers C(n,2)+1 to C(n+1,2); numbers in odd-numbered places form a decreasing sequence and the others an increasing sequence.
%H Michael De Vlieger, <a href="/A057028/b057028.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e Rows: 1; 3,2; 5,6,4; 9,8,10,7; ...
%t nn = 12; t = Table[Range[Binomial[n, 2] + 1, Binomial[n + 1, 2]], {n, nn}]; Reverse /@ Table[t[[n, If[OddQ@ k, Ceiling[k/2], -k/2] ]], {n, nn}, {k, n}] // Flatten (* _Michael De Vlieger_, Jul 02 2016 *)
%Y Reflection of the array in A057027 about its central column, a permutation of the natural numbers.
%Y Inverse permutation: A064789.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Jul 28, 2000