login
A351008
Alternately strict partitions. Number of even-length integer partitions y of n such that y_i > y_{i+1} for all odd i.
12
1, 0, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 23, 28, 34, 41, 50, 60, 71, 85, 102, 120, 142, 168, 197, 231, 271, 316, 369, 429, 497, 577, 668, 770, 888, 1023, 1175, 1348, 1545, 1767, 2020, 2306, 2626, 2990, 3401, 3860, 4379, 4963, 5616, 6350, 7173, 8093
OFFSET
0,6
FORMULA
Conjecture: a(n+1) = A122129(n+1) - A122130(n). - Gus Wiseman, Feb 21 2022
EXAMPLE
The a(3) = 1 through a(13) = 12 partitions (A..C = 10..12):
21 31 32 42 43 53 54 64 65 75 76
41 51 52 62 63 73 74 84 85
61 71 72 82 83 93 94
3221 81 91 92 A2 A3
4221 4321 A1 B1 B2
5221 4331 4332 C1
5321 5331 5332
6221 5421 5431
6321 6331
7221 6421
7321
8221
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], EvenQ[Length[#]]&&And@@Table[#[[i]]!=#[[i+1]], {i, 1, Length[#]-1, 2}]&]], {n, 0, 30}]
CROSSREFS
The version for equal instead of unequal is A035363.
The alternately equal and unequal version is A035457, any length A351005.
This is the even-length case of A122129, opposite A122135.
The odd-length version appears to be A122130.
The alternately unequal and equal version is A351007, any length A351006.
Sequence in context: A092833 A280664 A100926 * A258875 A179241 A316082
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 31 2022
STATUS
approved