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A342496
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Number of integer partitions of n with constant (equal) first quotients.
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8
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1, 1, 2, 3, 4, 4, 6, 6, 7, 7, 8, 7, 11, 9, 11, 12, 12, 10, 14, 12, 15, 16, 14, 13, 19, 15, 17, 17, 20, 16, 23, 19, 21, 20, 20, 22, 26, 21, 23, 25, 28, 22, 30, 24, 27, 29, 26, 25, 33, 29, 30, 29, 32, 28, 34, 31, 36, 34, 32, 31, 42
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OFFSET
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0,3
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COMMENTS
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The first quotients of a sequence are defined as if the sequence were an increasing divisor chain, so for example the first quotients of (6,3,1) are (1/2,1/3).
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LINKS
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FORMULA
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EXAMPLE
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The partition (12,6,3) has first quotients (1/2,1/2) so is counted under a(21).
The a(1) = 1 through a(9) = 7 partitions:
1 2 3 4 5 6 7 8 9
11 21 22 32 33 43 44 54
111 31 41 42 52 53 63
1111 11111 51 61 62 72
222 421 71 81
111111 1111111 2222 333
11111111 111111111
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], SameQ@@Divide@@@Partition[#, 2, 1]&]], {n, 0, 30}]
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CROSSREFS
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The version for differences instead of quotients is A049988.
The Heinz numbers of these partitions are A342522.
A000005 counts constant partitions.
A167865 counts strict chains of divisors > 1 summing to n.
Cf. A000837, A002843, A003242, A074206, A175342, A318991, A318992, A325557, A342527, A342528, A342529.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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