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 A279561 Number of length n inversion sequences avoiding the patterns 101, 102, 201, and 210. 23
 1, 1, 2, 6, 21, 77, 287, 1079, 4082, 15522, 59280, 227240, 873886, 3370030, 13027730, 50469890, 195892565, 761615285, 2965576715, 11563073315, 45141073925, 176423482325, 690215089745, 2702831489825, 10593202603775, 41550902139551, 163099562175851 (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. This is the same as the set of length n inversion sequences avoiding 101, 102, 201, and 210. It is conjectured that a_n also counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 021 and 120. LINKS Shane Chern, On 0012-avoiding inversion sequences and a Conjecture of Lin and Ma, arXiv:2006.04318 [math.CO], 2020. Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016. Chunyan Yan, Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019. FORMULA a(n) = 1 + Sum_{i=1..n-1} binomial(2i, i-1). a(n) = 1 + A057552(n-2). G.f.: (1-4*x+sqrt(-16*x^3+20*x^2-8*x+1))/(2*(x-1)*(4*x-1)). D-finite with recurrence: n*a(n) +(-7*n+6)*a(n-1) +2*(7*n-13)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Feb 21 2020 EXAMPLE The length 4 inversion sequences avoiding (101, 102, 201, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123. The length 4 inversion sequences avoiding (021, 120) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0022, 0023, 0100, 0101, 0102, 0103, 0110, 0111, 0112, 0113, 0122, 0123. MAPLE a:= proc(n) option remember; `if`(n<3, 1+n*(n-1)/2,       ((5*n^2-12*n+6)*a(n-1)-(4*n^2-10*n+6)*a(n-2))/((n-2)*n))     end: seq(a(n), n=0..30);  # Alois P. Heinz, Jan 18 2017 MATHEMATICA a[n_] := 1 + Sum[Binomial[2i, i-1], {i, 0, n-1}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 28 2017 *) CROSSREFS Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573. Sequence in context: A101265 A101879 A242622 * A294048 A063023 A150188 Adjacent sequences:  A279558 A279559 A279560 * A279562 A279563 A279564 KEYWORD nonn AUTHOR Megan A. Martinez, Jan 17 2017 STATUS approved

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Last modified October 21 21:51 EDT 2021. Contains 348155 sequences. (Running on oeis4.)