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A348540
Number of partitions of n into 3 parts whose smallest part divides the largest part.
0
0, 0, 1, 1, 2, 3, 3, 4, 6, 6, 6, 9, 9, 10, 12, 12, 13, 16, 15, 18, 20, 19, 19, 24, 25, 25, 27, 28, 28, 33, 31, 34, 37, 36, 38, 42, 41, 42, 44, 47, 47, 52, 50, 53, 57, 54, 54, 61, 62, 64, 65, 66, 66, 71, 71, 74, 76, 75, 75, 84, 82, 83, 87, 87, 90, 93, 91, 94, 96, 99, 97, 106
OFFSET
1,5
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling((n-i-j)/j) + floor((n-i-j)/j)).
MATHEMATICA
a[n_] := Sum[1 - Ceiling[(n - i - j)/j] + Floor[(n - i - j)/j], {j, 1, Floor[n/3]}, {i, j, Floor[(n - j)/2]}]; Array[a, 100] (* Amiram Eldar, Oct 22 2021 *)
CROSSREFS
Sequence in context: A290585 A106464 A093003 * A118096 A296440 A181692
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 21 2021
STATUS
approved