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A357644
Number of integer compositions of n into parts that are alternately unequal and equal.
19
1, 1, 1, 3, 4, 7, 8, 13, 17, 25, 30, 44, 58, 77, 98, 142, 176, 245, 311, 426, 548, 758, 952, 1319, 1682, 2308, 2934, 4059, 5132, 7087, 9008, 12395, 15757, 21728, 27552, 38019, 48272, 66515, 84462, 116467, 147812, 203825, 258772, 356686, 452876, 624399, 792578
OFFSET
0,4
LINKS
EXAMPLE
The a(1) = 1 through a(7) = 13 compositions:
(1) (2) (3) (4) (5) (6) (7)
(12) (13) (14) (15) (16)
(21) (31) (23) (24) (25)
(211) (32) (42) (34)
(41) (51) (43)
(122) (411) (52)
(311) (1221) (61)
(2112) (133)
(322)
(511)
(2113)
(3112)
(12211)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], And@@Table[#[[i]]==#[[i+1]], {i, 2, Length[#]-1, 2}]&&And@@Table[#[[i]]!=#[[i+1]], {i, 1, Length[#]-1, 2}]&]], {n, 0, 10}]
CROSSREFS
Without equal relations we have A000213, equal only A027383.
Even-length opposite: A003242, ranked by A351010, partitions A035457.
The version for partitions is A351006.
The opposite version is A357643, partitions A351005.
A011782 counts compositions.
A357621 gives half-alternating sum of standard compositions, skew A357623.
A357645 counts compositions by half-alternating sum, skew A357646.
Sequence in context: A374962 A060023 A345531 * A120355 A114210 A073271
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 14 2022
EXTENSIONS
More terms from Alois P. Heinz, Oct 19 2022
STATUS
approved