A342769 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,... .
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, 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, 12, 5, 11, 6, 10, 7, 9, 8, 8, 1, 17, 2, 16, 3, 15, 4, 14, 5, 13, 6, 12, 7
Offset: 1
Examples
[1,13]
[1,11] [2,12]
[1,9] [2,10] [3,11]
[1,7] [2,8] [3, 9] [4,10]
[1,5] [2,6] [3,7] [4, 8] [5, 9]
[1,3] [2,4] [3,5] [4,6] [5, 7] [6, 8]
[1,1] [2,2] [3,3] [4,4] [5,5] [6, 6] [7, 7]
2k 2 4 6 8 10 12 14
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2k Nondecreasing partitions of 2k
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2 1,1
4 1,3,2,2
6 1,5,2,4,3,3
8 1,7,2,6,3,5,4,4
10 1,9,2,8,3,7,4,6,5,5
12 1,11,2,10,3,9,4,8,5,7,6,6
14 1,13,2,12,3,11,4,10,5,9,6,8,7,7
...
Formula
a(n) = k + (k^2 + k - m)*(-1)^n / 2, where k = round(sqrt(m)) and m = 2*floor((n+1)/2).