OFFSET
0,3
COMMENTS
These are partitions of n with all even multiplicities (or run-lengths), except possibly the last.
EXAMPLE
The a(1) = 1 through a(9) = 7 partitions:
1 2 3 4 5 6 7 8 9
11 111 22 221 33 331 44 333
1111 11111 222 22111 332 441
2211 1111111 2222 22221
111111 3311 33111
221111 2211111
11111111 111111111
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@Table[#[[i]]==#[[i+1]], {i, 1, Length[#]-1, 2}]&]], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 31 2022
STATUS
approved