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 A351643 Number of length n word structures with all distinct runs using exactly 3 symbols. 3
 0, 0, 1, 3, 12, 28, 81, 177, 410, 906, 1869, 4001, 8094, 16032, 32355, 62499, 120078, 227880, 436743, 805797, 1487920, 2751618, 5017143, 9063625, 16153560, 29066676, 51334289, 90784671, 157941132, 275244344, 478874505, 823848357, 1412686722, 2400778830, 4091929101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Permuting the symbols will not change the structure. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 EXAMPLE The a(3) = 1 word is 123. The a(4) = 3 words are 1123, 1223, 1233. The a(5) = 12 words are 11123, 11213, 11223, 11231, 11233, 12113, 12223, 12232, 12233, 12311, 12322, 12333. PROG (PARI) \\ See A351641 for R, S. seq(n)={my(q=S(n), c=3); sum(k=1, c, R(q^k-1)*binomial(c, k)*(-1)^(3-k))/c!} CROSSREFS Column k=3 of A351641. Cf. A351644. Sequence in context: A308669 A115549 A005995 * A034503 A026557 A124052 Adjacent sequences: A351640 A351641 A351642 * A351644 A351645 A351646 KEYWORD nonn AUTHOR Andrew Howroyd, Feb 16 2022 STATUS approved

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Last modified December 4 01:51 EST 2023. Contains 367541 sequences. (Running on oeis4.)