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 case is A035457.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 31 2022
STATUS
approved