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%I #6 Mar 28 2021 19:34:24
%S 1,1,3,1,2,2,5,1,4,2,3,3,7,1,6,2,5,3,4,4,9,1,8,2,7,3,6,4,5,5,11,1,10,
%T 2,9,3,8,4,7,5,6,6,13,1,12,2,11,3,10,4,9,5,8,6,7,7,15,1,14,2,13,3,12,
%U 4,11,5,10,6,9,7,8,8,17,1,16,2,15,3,14,4,13,5,12,6,11,7
%N Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < t <= s ordered by decreasing 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-(-1)^n)/2).
%F a(n) = A342769(A103889(n)).
%e [13,1]
%e [11,1] [12,2]
%e [9,1] [10,2] [11,3]
%e [7,1] [8,2] [9, 3] [10,4]
%e [5,1] [6,2] [7,3] [8, 4] [9, 5]
%e [3,1] [4,2] [5,3] [6,4] [7, 5] [8, 6]
%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 Decreasing partitions of 2k
%e --------------------------------------------------------------------------
%e 2 1,1
%e 4 3,1,2,2
%e 6 5,1,4,2,3,3
%e 8 7,1,6,2,5,3,4,4
%e 10 9,1,8,2,7,3,6,4,5,5
%e 12 11,1,10,2,9,3,8,4,7,5,6,6
%e 14 13,1,12,2,11,3,10,4,9,5,8,6,7,7
%e ...
%Y Cf. A000194, A052928, A103889, A339399, A339443, A342769.
%K nonn
%O 1,3
%A _Wesley Ivan Hurt_, Mar 28 2021
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