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A342194
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Number of strict compositions of n with equal differences, or strict arithmetic progressions summing to n.
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2
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1, 1, 1, 3, 3, 5, 7, 7, 7, 13, 11, 11, 17, 13, 15, 25, 17, 17, 29, 19, 23, 35, 25, 23, 39, 29, 29, 45, 33, 29, 55, 31, 35, 55, 39, 43, 65, 37, 43, 65, 51, 41, 77, 43, 51, 85, 53, 47, 85, 53, 65, 87, 61, 53, 99, 67, 67, 97, 67, 59, 119, 61, 71, 113, 75, 79, 123, 67, 79, 117
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OFFSET
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0,4
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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(9) = 13 compositions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8)
(2,1) (3,1) (2,3) (2,4) (2,5) (2,6) (2,7)
(3,2) (4,2) (3,4) (3,5) (3,6)
(4,1) (5,1) (4,3) (5,3) (4,5)
(1,2,3) (5,2) (6,2) (5,4)
(3,2,1) (6,1) (7,1) (6,3)
(7,2)
(8,1)
(1,3,5)
(2,3,4)
(4,3,2)
(5,3,1)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&], SameQ@@Differences[#]&]], {n, 0, 30}]
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CROSSREFS
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Strict compositions in general are counted by A032020.
A000726 counts partitions with alternating parts unequal.
A003242 counts anti-run compositions.
A224958 counts compositions with alternating parts unequal.
A342343 counts compositions with alternating parts strictly decreasing.
A342495 counts compositions with constant quotients.
A342527 counts compositions with alternating parts equal.
Cf. A000009, A001522, A002843, A049988, A062968, A070211, A114921, A325545, A325557, A342496, A342515, A342522.
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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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