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A351005
Number of integer partitions of n into parts that are alternately equal and unequal.
33
1, 1, 2, 1, 2, 2, 3, 2, 4, 2, 5, 4, 6, 4, 8, 5, 10, 6, 12, 8, 16, 9, 18, 12, 22, 14, 28, 16, 33, 20, 40, 24, 48, 28, 56, 34, 67, 40, 80, 46, 94, 56, 110, 64, 130, 75, 152, 88, 176, 102, 206, 118, 238, 138, 276, 159, 320, 182, 368, 210, 424, 242, 488, 276, 558
OFFSET
0,3
COMMENTS
Also partitions whose multiplicities are all 2's, except possibly for the last, which may be 1.
EXAMPLE
The a(1) = 1 through a(12) = 6 partitions (A..C = 10..12):
1 2 3 4 5 6 7 8 9 A B C
11 22 221 33 331 44 441 55 443 66
2211 332 442 551 552
3311 3322 33221 4422
4411 5511
332211
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@Table[#[[i]]==#[[i+1]], {i, 1, Length[#]-1, 2}]&&And@@Table[#[[i]]!=#[[i+1]], {i, 2, Length[#]-1, 2}]&]], {n, 0, 30}]
CROSSREFS
The even-length ordered version is A003242, ranked by A351010.
The even-length case is A035457.
Without equalities we have A122135, opposite A122129, even-length A122134.
The non-strict version is A351004, opposite A351003, even-length A035363.
The opposite version is A351006, even-length A351007.
Sequence in context: A283451 A372970 A172245 * A238781 A319439 A051275
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 31 2022
STATUS
approved