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 A351644 Number of length n word structures with all distinct runs using at most 3 symbols. 3
 1, 1, 2, 4, 9, 21, 46, 108, 223, 487, 1028, 2060, 4327, 8591, 16818, 33562, 64441, 122983, 232378, 443446, 816371, 1503517, 2775372, 5052186, 9116047, 16231929, 29182198, 51503788, 91032821, 158301653, 275776810, 479642780, 824964483, 1414293391, 2403093256, 4095230980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Permuting the symbols will not change the structure. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A351018(n) + A351643(n). a(n) = Sum_{k=0..3} A351641(n,k). EXAMPLE The a(1) = 1 word is 1. The a(2) = 2 words are 11, 12. The a(3) = 4 words are 111, 112, 122, 123. The a(4) = 9 words are 1111, 1112, 1121, 1122, 1211, 1222, 1123, 1223, 1233. PROG (PARI) \\ See A351641 for R, S. seq(n)={my(q=S(n), c=3); concat([1], sum(k=1, c, R(q^k-1)*sum(r=k, c, binomial(r, k)*(-1)^(r-k)/r!) )); } CROSSREFS Cf. A351018, A351641, A351643. Sequence in context: A093698 A091619 A061439 * A027711 A307548 A084634 Adjacent sequences: A351641 A351642 A351643 * A351645 A351646 A351647 KEYWORD nonn AUTHOR Andrew Howroyd, Feb 16 2022 STATUS approved

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Last modified February 22 19:33 EST 2024. Contains 370260 sequences. (Running on oeis4.)