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A343248
Number of partitions of n into 3 parts such that no part divides n.
0
0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 5, 0, 8, 4, 4, 3, 16, 3, 21, 5, 14, 18, 33, 3, 31, 29, 30, 20, 56, 13, 65, 31, 52, 59, 59, 20, 96, 78, 80, 40, 120, 49, 133, 82, 83, 124, 161, 50, 156, 116, 154, 129, 208, 109, 181, 119, 200, 213, 261, 80, 280, 248, 204, 196, 267, 193, 341, 255
OFFSET
1,11
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - sign(c(i/j) + c((n-i-j)/j) + c((n-i-j)/i))), where c(n) = 1 - ceiling(n) + floor(n).
EXAMPLE
a(10) = 1; [4,3,3];
a(11) = 5; [7,2,2], [6,3,2], [5,4,2], [5,3,3], [4,4,3];
a(12) = 0; (Every partition of 12 into 3 parts contains at least one part that divides 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].);
a(13) = 8; [9,2,2], [8,3,2], [7,4,2], [6,5,2], [7,3,3], [6,4,3], [5,5,3], [5,4,4].
CROSSREFS
Cf. A343126.
Sequence in context: A371507 A143821 A099219 * A201288 A011441 A372391
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 08 2021
STATUS
approved