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A342913
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,... .
1
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, 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, 4, 11, 5, 10, 6, 9, 7, 8, 8, 17, 1, 16, 2, 15, 3, 14, 4, 13, 5, 12, 6, 11, 7
OFFSET
1,3
FORMULA
a(n) = k - (k^2 + k - m)*(-1)^n / 2, where k = round(sqrt(m)) and m = 2*floor((n+1-(-1)^n)/2).
a(n) = A342769(A103889(n)).
EXAMPLE
[13,1]
[11,1] [12,2]
[9,1] [10,2] [11,3]
[7,1] [8,2] [9, 3] [10,4]
[5,1] [6,2] [7,3] [8, 4] [9, 5]
[3,1] [4,2] [5,3] [6,4] [7, 5] [8, 6]
[1,1] [2,2] [3,3] [4,4] [5,5] [6, 6] [7, 7]
2k 2 4 6 8 10 12 14
--------------------------------------------------------------------------
2k Decreasing partitions of 2k
--------------------------------------------------------------------------
2 1,1
4 3,1,2,2
6 5,1,4,2,3,3
8 7,1,6,2,5,3,4,4
10 9,1,8,2,7,3,6,4,5,5
12 11,1,10,2,9,3,8,4,7,5,6,6
14 13,1,12,2,11,3,10,4,9,5,8,6,7,7
...
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Mar 28 2021
STATUS
approved