A343248 Number of partitions of n into 3 parts such that no part divides n.

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

Links

Table of n, a(n) for n=1..68.

Index entries for sequences related to partitions

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

Adjacent sequences: A343245 A343246 A343247 * A343249 A343250 A343251

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 08 2021

Status

approved