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A343270
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Number of partitions of n into 3 parts x,y,z such that (x+y+z) | x*y*z.
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3
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0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 3, 0, 3, 4, 5, 0, 6, 0, 6, 6, 5, 0, 11, 2, 6, 7, 9, 0, 23, 0, 11, 10, 8, 12, 15, 0, 9, 12, 21, 0, 34, 0, 15, 19, 11, 0, 41, 4, 18, 16, 18, 0, 36, 20, 31, 18, 14, 0, 61, 0, 15, 28, 33, 24, 56, 0, 24, 22, 65, 0, 48, 0, 18, 32, 27, 30, 67, 0, 77
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OFFSET
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1,10
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LINKS
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Table of n, a(n) for n=1..80.
Index entries for sequences related to partitions
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FORMULA
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a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(i*j*(n-i-j)/n) + floor(i*j*(n-i-j)/n)).
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EXAMPLE
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a(9) = 1; [3,3,3];
a(10) = 2; [1,4,5], [2,3,5];
a(11) = 0;
a(12) = 3; [1,3,8], [2,4,6], [3,4,5].
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MATHEMATICA
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Table[Sum[Sum[(1 - Ceiling[i*j*(n - i - j)/n] + Floor[i*j*(n - i - j)/n]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]
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CROSSREFS
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Sequence in context: A337980 A343309 A343488 * A137303 A049084 A234580
Adjacent sequences: A343267 A343268 A343269 * A343271 A343272 A343273
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KEYWORD
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nonn
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AUTHOR
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Wesley Ivan Hurt, Apr 09 2021
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STATUS
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approved
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