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 A279563 Number of length n inversion sequences avoiding the patterns 102, 201, and 210. 23
 1, 1, 2, 6, 22, 85, 328, 1253, 4754, 17994, 68158, 258808, 985906, 3768466, 14451386, 55585014, 214377618, 828795169, 3211030684, 12464308997, 48465092366, 188733879657, 735977084412, 2873525548315, 11231884145434, 43947466923095, 172115939825516 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_j <> e_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 102, 201, and 210. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1664 Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016. EXAMPLE The length 4 inversion sequences avoiding (102, 201, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123. MAPLE a:= proc(n) option remember; `if`(n<4, n!,       ((2*(12*n^3-91*n^2+213*n-149))*a(n-1)       -(3*(21*n^3-162*n^2+392*n-291))*a(n-2)       +(2*(33*n^3-257*n^2+633*n-484))*a(n-3)       -(4*(2*n-7))*(3*n^2-13*n+13)*a(n-4))        / ((n-1)*(3*n^2-19*n+29)))     end: seq(a(n), n=0..30);  # Alois P. Heinz, Feb 22 2017 MATHEMATICA a[n_] := a[n] = If[n < 4, n!, ((2*(12*n^3 - 91*n^2 + 213*n - 149))*a[n-1] - (3*(21*n^3 - 162*n^2 + 392*n - 291))*a[n-2] + (2*(33*n^3 - 257*n^2 + 633*n - 484))*a[n-3] - (4*(2*n - 7))*(3*n^2 - 13*n + 13)*a[n-4]) / ((n - 1)*(3*n^2 - 19*n + 29))]; Array[a, 30, 0] (* Jean-François Alcover, Nov 06 2017, after Alois P. Heinz *) CROSSREFS Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573. Sequence in context: A150245 A150246 A055700 * A150247 A150248 A105871 Adjacent sequences:  A279560 A279561 A279562 * A279564 A279565 A279566 KEYWORD nonn AUTHOR Megan A. Martinez, Feb 09 2017 EXTENSIONS a(10)-a(26) from Alois P. Heinz, Feb 22 2017 STATUS approved

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Last modified February 21 20:20 EST 2020. Contains 332110 sequences. (Running on oeis4.)