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A364060
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Triangle read by rows where T(n,k) is the number of integer partitions of n with rounded mean k.
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1
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1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 0, 2, 4, 0, 0, 1, 0, 2, 5, 3, 0, 0, 1, 0, 4, 7, 0, 3, 0, 0, 1, 0, 4, 8, 5, 4, 0, 0, 0, 1, 0, 4, 14, 7, 4, 0, 0, 0, 0, 1, 0, 7, 21, 8, 0, 5, 0, 0, 0, 0, 1, 0, 7, 22, 11, 10, 0, 5, 0, 0, 0, 0, 1
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OFFSET
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0,12
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COMMENTS
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We use the "rounding half to even" rule, see link.
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LINKS
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EXAMPLE
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Triangle begins:
1
0 1
0 1 1
0 1 1 1
0 2 2 0 1
0 2 4 0 0 1
0 2 5 3 0 0 1
0 4 7 0 3 0 0 1
0 4 8 5 4 0 0 0 1
0 4 14 7 4 0 0 0 0 1
0 7 21 8 0 5 0 0 0 0 1
0 7 22 11 10 0 5 0 0 0 0 1
0 7 36 15 12 0 6 0 0 0 0 0 1
0 12 32 36 14 0 6 0 0 0 0 0 0 1
0 12 53 23 23 16 0 7 0 0 0 0 0 0 1
0 12 80 30 27 19 0 0 7 0 0 0 0 0 0 1
Row n = 7 counts the following partitions:
. (31111) (511) . (61) . . (7)
(22111) (421) (52)
(211111) (4111) (43)
(1111111) (331)
(322)
(3211)
(2221)
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MATHEMATICA
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Table[If[n==k==0, 1, Length[Select[IntegerPartitions[n], Round[Mean[#]]==k&]]], {n, 0, 15}, {k, 0, n}]
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CROSSREFS
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The rank statistic for this triangle is A363489.
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KEYWORD
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AUTHOR
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STATUS
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approved
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