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A343247
Number of partitions of n into 3 parts where at least 1 part divides n.
0
0, 0, 1, 1, 2, 3, 3, 5, 6, 7, 5, 12, 6, 12, 15, 18, 8, 24, 9, 28, 23, 22, 11, 45, 21, 27, 31, 45, 14, 62, 15, 54, 39, 37, 43, 88, 18, 42, 47, 93, 20, 98, 21, 79, 86, 52, 23, 142, 44, 92, 63, 96, 26, 134, 71, 142, 71, 67, 29, 220, 30, 72, 127, 145, 85, 170, 33, 130, 87, 185
OFFSET
1,5
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(c(n/j) + c(n/i) + c(n/(n-i-j))), where c(n) = 1 - ceiling(n) + floor(n).
EXAMPLE
a(6) = 3; [1,1,4], [1,2,3], [2,2,2];
a(7) = 3; [5,1,1], [4,2,1], [3,3,1];
a(8) = 5; [6,1,1], [5,2,1], [4,3,1], [3,2,2], [3,3,2];
a(12) = 12; [10,1,1], [9,2,1], [8,3,1], [7,4,1], [6,5,1], [8,2,2], [7,3,2], [6,4,2], [5,5,2], [6,3,3], [5,4,3], [4,4,4].
CROSSREFS
Cf. A343126.
Sequence in context: A344705 A331170 A325183 * A097248 A097247 A097246
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 08 2021
STATUS
approved