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A329738
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Number of compositions of n whose run-lengths are all equal.
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50
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1, 1, 2, 4, 6, 8, 19, 24, 45, 75, 133, 215, 401, 662, 1177, 2035, 3587, 6190, 10933, 18979, 33339, 58157, 101958, 178046, 312088, 545478, 955321, 1670994, 2925717, 5118560, 8960946, 15680074, 27447350, 48033502, 84076143, 147142496, 257546243, 450748484, 788937192
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OFFSET
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0,3
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COMMENTS
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A composition of n is a finite sequence of positive integers with sum n.
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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(6) = 19 compositions:
(1) (2) (3) (4) (5) (6)
(11) (12) (13) (14) (15)
(21) (22) (23) (24)
(111) (31) (32) (33)
(121) (41) (42)
(1111) (131) (51)
(212) (123)
(11111) (132)
(141)
(213)
(222)
(231)
(312)
(321)
(1122)
(1212)
(2121)
(2211)
(111111)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Length/@Split[#]&]], {n, 0, 10}]
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PROG
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(PARI) seq(n)={my(b=Vec(1/(1 - sum(k=1, n, x^k/(1+x^k) + O(x*x^n)))-1)); concat([1], vector(n, k, sumdiv(k, d, b[d])))} \\ Andrew Howroyd, Dec 30 2020
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CROSSREFS
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Compositions with relatively prime run-lengths are A000740.
Compositions with equal multiplicities are A098504.
Compositions with equal differences are A175342.
Compositions with distinct run-lengths are A329739.
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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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