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%I #9 May 09 2021 12:56:29
%S 1,1,1,3,2,2,1,5,2,4,3,3,1,7,2,6,3,5,4,4,1,9,2,8,3,7,4,6,5,5,1,11,2,
%T 10,3,9,4,8,5,7,6,6,1,13,2,12,3,11,4,10,5,9,6,8,7,7,1,15,2,14,3,13,4,
%U 12,5,11,6,10,7,9,8,8,1,17,2,16,3,15,4,14,5,13,6,12,7
%N Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < s <= t ordered by increasing values of s and where k = 1,2,... .
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = k + (k^2 + k - m)*(-1)^n / 2, where k = round(sqrt(m)) and m = 2*floor((n+1)/2).
%F a(n) = A342913(A103889(n)). - _Wesley Ivan Hurt_, May 09 2021
%e [1,13]
%e [1,11] [2,12]
%e [1,9] [2,10] [3,11]
%e [1,7] [2,8] [3, 9] [4,10]
%e [1,5] [2,6] [3,7] [4, 8] [5, 9]
%e [1,3] [2,4] [3,5] [4,6] [5, 7] [6, 8]
%e [1,1] [2,2] [3,3] [4,4] [5,5] [6, 6] [7, 7]
%e 2k 2 4 6 8 10 12 14
%e --------------------------------------------------------------------------
%e 2k Nondecreasing partitions of 2k
%e --------------------------------------------------------------------------
%e 2 1,1
%e 4 1,3,2,2
%e 6 1,5,2,4,3,3
%e 8 1,7,2,6,3,5,4,4
%e 10 1,9,2,8,3,7,4,6,5,5
%e 12 1,11,2,10,3,9,4,8,5,7,6,6
%e 14 1,13,2,12,3,11,4,10,5,9,6,8,7,7
%e ...
%Y Cf. A000194, A052928, A103889, A339399, A339443, A342913.
%K nonn,tabf
%O 1,4
%A _Wesley Ivan Hurt_, Mar 21 2021
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