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A351593 Number of odd-length integer partitions of n into parts that are alternately equal and strictly decreasing. 4
0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 3, 5, 4, 6, 4, 8, 6, 9, 6, 12, 7, 14, 10, 16, 11, 20, 13, 24, 16, 28, 18, 34, 21, 40, 26, 46, 30, 56, 34, 64, 41, 75, 48, 88, 54, 102, 64, 118, 73, 138, 84, 159, 98, 182, 112, 210, 128, 242, 148, 276, 168, 318 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
Also odd-length partitions whose run-lengths are all 2's, except for the last, which is 1.
LINKS
EXAMPLE
The a(1) = 1 through a(15) = 6 partitions (A..F = 10..15):
1 2 3 4 5 6 7 8 9 A B C D E F
221 331 332 441 442 443 552 553 554 663
551 661 662 771
33221 44221 44331
55221
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]]&&And@@Table[If[EvenQ[i], #[[i]]!=#[[i+1]], #[[i]]==#[[i+1]]], {i, Length[#]-1}]&]], {n, 0, 30}]
CROSSREFS
The even-length ordered version is A003242, ranked by A351010.
The opposite version is A053251, even-length A351007, any length A351006.
This is the odd-length case of A351005, even-length A035457.
With only equalities we get:
- opposite any length: A351003
- opposite odd-length: A000009 (except at 0)
- opposite even-length: A351012
- any length: A351004
- odd-length: A351594
- even-length: A035363
Without equalities we get:
- opposite any length: A122129 (apparently)
- opposite odd-length: A122130 (apparently)
- opposite even-length: A351008
- any length: A122135 (apparently)
- odd-length: A351595
- even-length: A122134 (apparently)
Sequence in context: A103858 A010554 A062610 * A025801 A060548 A140426
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 23 2022
STATUS
approved

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Last modified March 28 13:17 EDT 2024. Contains 371254 sequences. (Running on oeis4.)