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 A293742 Number of sets of nonempty words with a total of n letters over ternary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter. 4
 1, 1, 2, 6, 14, 39, 104, 284, 775, 2145, 5941, 16563, 46329, 130100, 366432, 1035191, 2931797, 8323290, 23680142, 67505721, 192791938, 551537506, 1580315319, 4534715008, 13030197881, 37489497472, 107991978290, 311433926717, 899093131819, 2598257241179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: Product_{j>=1} (1+x^j)^A001006(j). MAPLE g:= proc(n) option remember; `if`(n<2, 1,       g(n-1)+add(g(k)*g(n-k-2), k=0..n-2))     end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(b(n-i*j, i-1)*binomial(g(i), j), j=0..n/i)))     end: a:= n-> b(n\$2): seq(a(n), n=0..35); MATHEMATICA With[{n = 29}, CoefficientList[Series[Product[(1 + x^j)^Hypergeometric2F1[(1 - j)/2, -j/2, 2, 4], {j, n}], {x, 0, n}], x]] (* Michael De Vlieger, Oct 15 2017, after Peter Luschny at A001006 *) PROG (Python) from sympy.core.cache import cacheit from sympy import binomial @cacheit def g(n): return 1 if n<2 else g(n - 1) + sum(g(k)*g(n - k - 2) for k in range(n - 1)) @cacheit def b(n, i): return 1 if n==0 else 0 if i<1 else sum(b(n - i*j, i - 1)*binomial(g(i), j) for j in range(n//i + 1)) def a(n): return b(n, n) print([a(n) for n in range(36)]) # Indranil Ghosh, Oct 15 2017 CROSSREFS Column k=3 of A293112. Cf. A001006. Sequence in context: A263734 A263735 A263731 * A299119 A271895 A151538 Adjacent sequences:  A293739 A293740 A293741 * A293743 A293744 A293745 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 15 2017 STATUS approved

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Last modified May 7 22:52 EDT 2021. Contains 343652 sequences. (Running on oeis4.)