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A357644
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Number of integer compositions of n into parts that are alternately unequal and equal.
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19
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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
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OFFSET
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0,4
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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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}]
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CROSSREFS
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The version for partitions is A351006.
A357621 gives half-alternating sum of standard compositions, skew A357623.
Cf. A001590, A029862, A035544, A097805, A122129, A122134, A122135, A351003, A351004, A351007, A357136, A357641.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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