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A338528 Number of partitions of k*n into two parts (s,t) such that s <= t and t | k*s for k = 1..n. 0
0, 2, 2, 5, 4, 11, 7, 13, 11, 19, 11, 27, 15, 28, 30, 34, 20, 45, 23, 52, 46, 49, 28, 71, 45, 58, 54, 78, 37, 105, 42, 81, 77, 79, 85, 124, 51, 90, 91, 137, 57, 156, 61, 134, 143, 115, 67, 178, 102, 160, 128, 162, 75, 187, 150, 206, 144, 143, 84, 276, 91, 156, 213, 199, 181, 263 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=1..n} Sum_{i=1..floor(n*k/2)} (1 - ceiling(k*i/(k*n-i)) + floor(k*i/(k*n-i))).
EXAMPLE
a(6) = 11; The 11 partitions of 6*1, 6*2, ..., 6*6 into 2 parts (s,t) such that s <= t and t | k*s for k = 1..n are:
6: (3,3),
12: (4,8), (6,6),
18: (9,9),
24: (8,16), (12,12),
30: (5,25), (15,15),
36: (9,24), (12,24), (18,18).
MATHEMATICA
Table[Sum[Sum[(1 - Ceiling[k*i/(k*n - i)] + Floor[k*i/(k*n - i)]), {i, Floor[k*n/2]}], {k, n}], {n, 50}]
CROSSREFS
Cf. A338021.
Sequence in context: A112472 A240412 A292263 * A238624 A124506 A264687
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Nov 07 2020
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)