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A342527
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Number of compositions of n with alternating parts equal.
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18
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1, 1, 2, 4, 6, 8, 11, 12, 16, 17, 21, 20, 29, 24, 31, 32, 38, 32, 46, 36, 51, 46, 51, 44, 69, 51, 61, 60, 73, 56, 87, 60, 84, 74, 81, 76, 110, 72, 91, 88, 115, 80, 123, 84, 117, 112, 111, 92, 153, 101, 132, 116, 139, 104, 159, 120, 161, 130, 141, 116, 205, 120, 151, 156, 178, 142, 195, 132, 183, 158
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OFFSET
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0,3
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COMMENTS
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These are finite sequences q of positive integers summing to n such that q(i) = q(i+2) for all possible i.
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(8) = 16 compositions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (12) (13) (14) (15) (16) (17)
(21) (22) (23) (24) (25) (26)
(111) (31) (32) (33) (34) (35)
(121) (41) (42) (43) (44)
(1111) (131) (51) (52) (53)
(212) (141) (61) (62)
(11111) (222) (151) (71)
(1212) (232) (161)
(2121) (313) (242)
(111111) (12121) (323)
(1111111) (1313)
(2222)
(3131)
(21212)
(11111111)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Plus@@@Reverse/@Partition[#, 2, 1]&]], {n, 0, 15}]
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CROSSREFS
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The version with alternating parts unequal is A224958 (unordered: A000726).
The version with alternating parts weakly decreasing is A342528.
A000005 counts constant compositions.
A000041 counts weakly increasing (or weakly decreasing) compositions.
A002843 counts compositions with all adjacent parts x <= 2y.
A003242 counts anti-run compositions.
A175342 counts compositions with constant differences.
A342495 counts compositions with constant first quotients.
Cf. A001522, A008965, A048004, A059966, A064410, A064428, A069916, A114921, A167606, A325545, A325557.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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