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A342515 Number of strict partitions of n with constant (equal) first-quotients. 9
1, 1, 1, 2, 2, 3, 3, 5, 4, 5, 5, 6, 6, 8, 8, 9, 8, 9, 9, 11, 10, 13, 11, 12, 12, 13, 14, 14, 15, 15, 16, 18, 16, 17, 17, 19, 18, 20, 20, 22, 21, 21, 23, 23, 22, 24, 23, 24, 24, 27, 25, 26, 27, 27, 27, 28, 29, 31, 29, 30, 31, 32, 33, 35, 32, 35, 33, 35, 34, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Also the number of reversed strict partitions of n with constant (equal) first-quotients.
The first quotients of a sequence are defined as if the sequence were an increasing divisor chain, so for example the quotients of (6,3,1) are (1/2,1/3).
LINKS
EXAMPLE
The a(1) = 1 through a(15) = 9 partitions (A..F = 10..15):
1 2 3 4 5 6 7 8 9 A B C D E F
21 31 32 42 43 53 54 64 65 75 76 86 87
41 51 52 62 63 73 74 84 85 95 96
61 71 72 82 83 93 94 A4 A5
421 81 91 92 A2 A3 B3 B4
A1 B1 B2 C2 C3
C1 D1 D2
931 842 E1
8421
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&SameQ@@Divide@@@Partition[#, 2, 1]&]], {n, 0, 30}]
CROSSREFS
The version for differences instead of quotients is A049980.
The non-strict ordered version is A342495.
The non-strict version is A342496.
The distinct instead of equal version is A342520.
A000005 counts constant partitions.
A000041 counts partitions (strict: A000009).
A001055 counts factorizations (strict: A045778, ordered: A074206).
A003238 counts chains of divisors summing to n - 1 (strict: A122651).
A154402 counts partitions with adjacent parts x = 2y.
A167865 counts strict chains of divisors > 1 summing to n.
A175342 counts compositions with equal differences.
Sequence in context: A332893 A113605 A369984 * A307815 A070230 A007150
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 19 2021
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)