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 A329738 Number of compositions of n whose run-lengths are all equal. 23
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers with sum n. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{d|n} A003242(d). a(n) = A329745(n) + A000005(n). EXAMPLE 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) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Length/@Split[#]&]], {n, 0, 10}] PROG (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 CROSSREFS 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. Cf. A003242, A008965, A107429, A164707, A238130, A242882, A274174, A329745, A329766. Sequence in context: A104001 A048784 A152491 * A133296 A323333 A076402 Adjacent sequences:  A329735 A329736 A329737 * A329739 A329740 A329741 KEYWORD nonn AUTHOR Gus Wiseman, Nov 20 2019 STATUS approved

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)