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A348537
Number of partitions of n into 3 parts whose largest part divides n.
1
0, 0, 1, 1, 0, 2, 0, 2, 1, 2, 0, 4, 0, 3, 1, 4, 0, 5, 0, 5, 1, 5, 0, 7, 0, 6, 1, 7, 0, 8, 0, 8, 1, 8, 0, 10, 0, 9, 1, 10, 0, 11, 0, 11, 1, 11, 0, 13, 0, 12, 1, 13, 0, 14, 0, 14, 1, 14, 0, 16, 0, 15, 1, 16, 0, 17, 0, 17, 1, 17, 0, 19, 0, 18, 1, 19, 0, 20, 0, 20, 1, 20, 0, 22, 0
OFFSET
1,6
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(n/(n-i-j)) + floor(n/(n-i-j))).
MATHEMATICA
Array[Sum[Sum[(1 - Ceiling[#/(# - i - j)] + Floor[#/(# - i - j)]), {i, j, Floor[(# - j)/2]} ], {j, Floor[#/3]} ] &, 85] (* Michael De Vlieger, Oct 21 2021 *)
PROG
(PARI) A348537(n) = sum(j=1, (n\3), sum(i=j, ((n-j)\2), (1 - ceil(n/(n-i-j)) + floor(n/(n-i-j))))); \\ Antti Karttunen, Feb 18 2023
CROSSREFS
Cf. A069905.
Sequence in context: A378216 A070824 A174725 * A071459 A319164 A070288
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 21 2021
STATUS
approved