A263777 -id:A263777 - cp's OEIS frontend

A263778 Number of inversion sequences avoiding pattern 120.

1, 1, 2, 6, 23, 103, 515, 2803, 16334, 100700, 650905, 4380595, 30528410, 219352058, 1619260140, 12245357074, 94636062782, 745907086918, 5985448211508, 48824435255942, 404330087326924, 3395418226577756, 28884708430087203, 248696210256230427

Offset: 0

Michel Marcus, Oct 26 2015

nonn

Number of length n inversion sequences avoiding e_k < e_i < e_j for iAlois P. Heinz, Dec 20 2016

Jay Pantone, Table of n, a(n) for n = 0..200
Sylvie Corteel, Megan A. Martinez, Carla D. Savage, and Michael Weselcouch, Patterns in Inversion Sequences I, arXiv:1510.05434 [math.CO], 2015.
Toufik Mansour and Mark Shattuck, Pattern Avoidance in Inversion Sequences, Pure Math. Appl. (PU.M.A.) 25 (2015), no. 2, 157-176.
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Jay Pantone, The enumeration of inversion sequences avoiding the patterns 201 and 210, arXiv:2310.19632 [math.CO], 2023.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024. See p. 2.

Cf. A263777, A263779, A263780.

a(0)=1 prepended by Alois P. Heinz, Dec 15 2016

a(10)-a(23) from Alois P. Heinz, Dec 20 2016

A263779 Number of inversion sequences avoiding pattern 010.

Original entry on oeis.org

1, 1, 2, 5, 15, 53, 215, 979, 4922, 26992, 159958, 1016784, 6890723, 49534501, 376081602, 3004503758, 25175290576, 220624253707, 2017049937115, 19195118759579, 189758808470023, 1945188215493411, 20642140342300062, 226427702583430619, 2563833140546044096

Offset: 0

Michel Marcus, Oct 26 2015

nonn

Benjamin Testart, Table of n, a(n) for n = 0..200
Sylvie Corteel, Megan A. Martinez, Carla D. Savage, and Michael Weselcouch, Patterns in Inversion Sequences I, arXiv:1510.05434 [math.CO], 2015.
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Jay Pantone, The enumeration of inversion sequences avoiding the patterns 201 and 210, arXiv:2310.19632 [math.CO], 2023.
Benjamin Testart, Inversion sequences avoiding the pattern 010, arXiv:2212.07222 [math.CO], 2022.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024. See p. 2.

Cf. A022493, A263777, A263778, A263780.

a(0), a(10)-a(17) from Alois P. Heinz, Dec 15 2016

A263780 Number of inversion sequences avoiding pattern 100.

Original entry on oeis.org

1, 1, 2, 6, 23, 106, 565, 3399, 22678, 165646, 1311334, 11161529, 101478038, 980157177, 10011461983, 107712637346, 1216525155129, 14380174353934, 177440071258827, 2280166654498540, 30450785320307436, 421820687108853017, 6050801956624661417, 89738550379292147192

Offset: 0

Michel Marcus, Oct 26 2015

nonn

Number of length n inversion sequences avoiding e_i > e_j = e_k for iAlois P. Heinz, Dec 19 2016

Jay Pantone, Table of n, a(n) for n = 0..200
Sylvie Corteel, Megan A. Martinez, Carla D. Savage, and Michael Weselcouch, Patterns in Inversion Sequences I, arXiv:1510.05434 [math.CO], 2015.
Ilias Kotsireas, Toufik Mansour, and Gökhan Yıldırım, An Algorithmic Approach Based on Generating Trees for Enumerating Pattern-Avoiding Inversion Sequences, J. Symbolic Comput. 120 (2024), Paper No. 102231, 18 pp.
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Jay Pantone, The enumeration of inversion sequences avoiding the patterns 201 and 210, arXiv:2310.19632 [math.CO], 2023.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024. See p. 2.

Cf. A263777, A263778, A263779, A279544.

a(0)=1 prepended by Alois P. Heinz, Dec 15 2016

a(10)-a(23) from Alois P. Heinz, Dec 19 2016

A279570 Number of length n inversion sequences avoiding the patterns 110 and 120.

Original entry on oeis.org

1, 1, 2, 6, 22, 92, 423, 2091, 10950, 60120, 343453, 2029809, 12354661, 77168197, 493189283, 3217459119, 21382723456, 144518555231, 991885282987, 6904454991721, 48691257834999, 347542736059492, 2508603139285095, 18297609829743478, 134772911886028731

Offset: 0

Megan A. Martinez, Feb 21 2017

nonn

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_k and e_i > e_k. This is the same as the set of length n inversion sequences avoiding 110 and 120.

			The length 4 inversion sequences avoiding (110,120) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0102, 0103, 0111, 0112, 0113, 0121, 0122, 0123.

Benjamin Testart, Table of n, a(n) for n = 0..350
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279571, A279572, A279573.

a(10)-a(24) from Alois P. Heinz, Feb 21 2017

A279559 Number of length n inversion sequences avoiding the patterns 010 and 120.

Original entry on oeis.org

1, 1, 2, 5, 15, 52, 201, 845, 3801, 18089, 90316, 470010, 2536077, 14127741, 80966690, 475979359, 2863157581, 17585971037, 110095460224, 701418693025, 4541497543092, 29847982448766, 198913925919741, 1342890255133042, 9176456969273844, 63422002415068463

Offset: 0

Megan A. Martinez, Jan 17 2017

nonn

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_k. This is the same as the set of length n inversion sequences avoiding 010 and 120.

			The length 4 inversion sequences avoiding (010, 120) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Benjamin Testart, Table of n, a(n) for n = 0..400
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Benjamin Testart, Inversion sequences avoiding the pattern 010, arXiv:2212.07222 [math.CO], 2022.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.
Chunyan Yan, Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019.

Cf. A000108, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

a(10)-a(25) from Alois P. Heinz, Feb 22 2017

A279555 Number of length n inversion sequences avoiding the patterns 110, 210, 120, and 010.

Original entry on oeis.org

1, 1, 2, 5, 15, 51, 189, 746, 3091, 13311, 59146, 269701, 1256820, 5966001, 28773252, 140695923, 696332678, 3483193924, 17589239130, 89575160517, 459648885327, 2374883298183, 12346911196912, 64555427595970, 339276669116222, 1791578092326881, 9501960180835998

Offset: 0

Megan A. Martinez, Dec 16 2016

nonn

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_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 110, 120, and 210.
It can be shown that this sequence also counts the 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 010, 100, 120, and 210.
From Andrei Asinowski, Jan 22 2025: (Start)
It also enumerates seven other classes of inversion sequences defined by avoidance of four patterns of length 3 (case 166 in Callan and Mansour).
It also enumerates inversion sequences that avoid the patterns 011 and 201, and inversion sequences that avoid the patterns 011 and 210.
For n >= 1, it also enumerates strong rectangulations that avoid T-shaped joints. (End)

			The length 3 inversion sequences avoiding (010, 110, 120, 210) are 000, 001, 002, 011, 012.
The length 4 inversion sequences avoiding (010, 110, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Jay Pantone, Table of n, a(n) for n = 0..500
Andrei Asinowski and Michaela A. Polley, Patterns in rectangulations. Part I: T-like patterns, inversion sequence classes I(010, 101, 120, 201) and I(011, 201), and rushed Dyck paths, arXiv:2501.11781 [math.CO], 2025.
David Callan and Toufik Mansour, Inversion sequences avoiding quadruple length-3 patterns, Integers, 23 (2023), Article A78.
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Jay Pantone, The enumeration of inversion sequences avoiding the patterns 201 and 210, Enumerative Combinatorics and Applications, 4:4 (2024), Article S2R25.
Chunyan Yan and Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019.

Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

a(n) ~ c * (1 + sqrt(2))^(2*n) / n^(3/2), where c = 0.00391075995650885016134430802... - Vaclav Kotesovec, Jan 23 2025

a(10)-a(26) from Alois P. Heinz, Jan 05 2017

A279564 Number of length n inversion sequences avoiding the patterns 000 and 100.

Original entry on oeis.org

1, 1, 2, 5, 16, 60, 260, 1267, 6850, 40572, 260812, 1805646, 13377274, 105487540, 881338060, 7770957903, 72060991394, 700653026744, 7123871583656, 75561097962918, 834285471737784, 9570207406738352, 113855103776348136, 1402523725268921870, 17863056512845724036, 234910502414771617316, 3185732802058088068444, 44501675392317774477088

Offset: 0

Megan A. Martinez, Feb 09 2017

nonn

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 000 and 100.

Benjamin Testart, Table of n, a(n) for n = 0..540
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.
Chunyan Yan and Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019.

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

b:= proc(n, i, m, s) option remember; `if`(n=0, 1, add(
      `if`(j in s, 0, b(n-1, i+1, max(m, j),
      `if`(j<=m, s union {j}, s))), j=1..i))
    end:
a:= n-> b(n, 1, 0, {}):
seq(a(n), n=0..15);  # Alois P. Heinz, Feb 22 2017

b[n_, i_, m_, s_List] := b[n, i, m, s] = If[n == 0, 1, Sum[If[MemberQ[s, j], 0, b[n-1, i+1, Max[m, j], If[j <= m, s ~Union~ {j}, s]]], {j, 1, i}] ]; a[n_] := b[n, 1, 0, {}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jul 10 2017, after Alois P. Heinz *)

The length 4 inversion sequences avoiding (000,100) are 0011, 0012, 0013, 0021, 0022, 0023, 0101, 0102, 0103, 0110, 0112, 0113, 0120, 0121, 0122, 0123.

a(10)-a(23) from Alois P. Heinz, Feb 22 2017

a(24)-a(27) from Vaclav Kotesovec, Oct 08 2021

A279566 Number of length n inversion sequences avoiding the patterns 102 and 201.

Original entry on oeis.org

1, 1, 2, 6, 22, 87, 354, 1465, 6154, 26223, 113236, 494870, 2185700, 9743281, 43784838, 198156234, 902374498, 4131895035, 19012201080, 87864535600, 407664831856, 1898184887679, 8867042353912, 41543375724751, 195164372948152, 919138464708907, 4338701289961694, 20524046955770940

Offset: 0

Megan A. Martinez, Feb 09 2017

nonn

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 and 201.

			The length 4 inversion sequences avoiding (102, 201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123

Benjamin Testart, Table of n, a(n) for n = 0..1400
Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016-2018.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.
Chunyan Yan, Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019.

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

G.f.: (-8*x^4 + 18*x^3 - 10*x^2 - 8*x + 4 + 2 * (2*x - 1) * (x^2 - 2*x + 2) * ((5*x - 1)*(x - 1))^(1/2)) / (4*x * (2*x - 1) * (x - 1) * (x - 2)^2). - Benjamin Testart, Jul 12 2024

a(n) ~ 41 * 5^(n + 3/2) / (648 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Nov 21 2024

a(10)-a(11) from Alois P. Heinz, Feb 24 2017
a(12)-a(17) from Bert Dobbelaere, Dec 30 2018
a(18) and beyond from Benjamin Testart, Jul 12 2024

A279557 Number of length n inversion sequences avoiding the patterns 110, 120, and 021.

Original entry on oeis.org

1, 1, 2, 6, 20, 68, 233, 805, 2807, 9879, 35073, 125513, 452389, 1641029, 5986994, 21954974, 80884424, 299233544, 1111219334, 4140813374, 15478839554, 58028869154, 218123355524, 821908275548, 3104046382352, 11747506651600, 44546351423300, 169227201341652

Offset: 0

Megan A. Martinez, Jan 16 2017

nonn

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_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 110, 120, and 021.

			The length 4 inversion sequences avoiding (110, 120, 021) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0022, 0023, 0100, 0101, 0102, 0103, 0111, 0112, 0113, 0122, 0123.

Alois P. Heinz, Table of n, a(n) for n = 0..1668
Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Murray Tannock, Equivalence classes of mesh patterns with a dominating pattern, MSc Thesis, Reykjavik Univ., May 2016.

Cf. A000108, A114277, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

a:= proc(n) option remember; `if`(n<3, n!,
      ((5*n^2-6*n-2)*a(n-1)-(4*n-2)*(n-1)*a(n-2))/(n^2-4))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 11 2017

a[n_] := 1 + Sum[(k - t - 1) (k - t)/(n - t + 1)* Binomial[2 n - k - t + 1, n - k + 1], {t, n - 1}, {k, t + 2, n + 1}]; Array[a, 28, 0] (* Robert G. Wilson v, Feb 25 2017 *)

a(n) = 1 + Sum_{t=1..n-1} Sum_{k=t+2..n+1} (k-t-1)*(k-t)/(n-t+1) * binomial(2n-k-t+1,n-k+1).
Conjecture: a(n) = C_{n+1}-Sum_{i=1..n} C_i where C_i is the i-th Catalan number, binomial(2i,i)/(i+1).
Assuming the conjecture a(n) ~ (64/3)*4^n/((4*n+7)^(3/2)*sqrt(Pi)). - Peter Luschny, Feb 24 2017
From Alois P. Heinz, Mar 11 2017: (Start)
a(n) = 1 + A114277(n-2) for n>1.
G.f.: (sqrt(1-4*x)+2*x-1)*(2*x-1)/(2*(1-x)*x^2). (End)
D-finite with recurrence: (n+2)*a(n) +(-7*n-4)*a(n-1) +2*(7*n-5)*a(n-2) +4*(-2*n+3)*a(n-3)=0. - R. J. Mathar, Feb 21 2020

a(10)-a(12) from Alois P. Heinz, Feb 24 2017

a(13) onward Robert G. Wilson v, Feb 25 2017

A279565 Number of length n inversion sequences avoiding the patterns 100, 110, 120, 201, and 210.

Original entry on oeis.org

1, 1, 2, 6, 21, 81, 332, 1420, 6266, 28318, 130412, 609808, 2887582, 13818590, 66726628, 324713196, 1590853485, 7840315329, 38843186366, 193342353214, 966409013021, 4848846341569, 24412146213116, 123290812268404, 624448756434476, 3171046361310556

Offset: 0

Megan A. Martinez, Feb 09 2017

nonn

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_k. This is the same as the set of length n inversion sequences avoiding 100, 110, 120, 201, and 210.

			The length 4 inversion sequences avoiding (100, 110, 120, 201, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0101, 0102, 0103, 0111, 0112, 0113, 0121, 0122, 0123.

Alois P. Heinz, Table of n, a(n) for n = 0..1372
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

I:=[6, 21, 81]; [1,1,2] cat [n le 3 select I[n] else ( (n+1)*(17*n+6)*Self(n-1) +(49*n^2+11*n+22)*Self(n-2) +3*(3*n-1)*(3*n-2)*Self(n-3) )/(5*(n+2)*(n+1)) : n in [1..30]]; // G. C. Greubel, Mar 29 2019

a:= proc(n) option remember; `if`(n<3, n!,
      ((n-1)*(17*n-28)*a(n-1) +(49*n^2-185*n+196)*a(n-2)
       +(3*(3*n-7))*(3*n-8)*a(n-3)) / (5*n*(n-1)))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 22 2017

a[n_] := a[n] = If[n < 3, n!, (((n - 1)*(17*n - 28)*a[n-1] + (49*n^2 - 185*n + 196)*a[n-2] + (3*(3*n - 7))*(3*n - 8)*a[n-3]) / (5*n*(n - 1)))]; Array[a, 30, 0] (* Jean-François Alcover, Nov 06 2017, after Alois P. Heinz *)
Join[{1}, Table[(1/n)*Sum[m*Sum[Binomial[k, n-m-k]*Binomial[n+k-1, k], {k, 0, n-m}], {m, 1, n}], {n, 1, 30}]] (* G. C. Greubel, Mar 29 2019 *)

a(n):=if n=0 then 1 else sum(m*sum(binomial(k,n-m-k)*binomial(n+k-1,k),k,0,n-m),m,1,n)/n; /* Vladimir Kruchinin, Mar 26 2019 */

my(x='x+O('x^30)); Vec(round(3/(4-4*sin(asin((27*x+11)/16)/3)))) \\ G. C. Greubel, Mar 29 2019

[1] +[(1/n)*(sum(sum(k*binomial(j,n-k-j)*binomial(n+j-1,j) for j in (0..n-k)) for k in (1..n))) for n in (1..30)] # G. C. Greubel, Mar 29 2019

G.f.: 3/(4-4*sin(asin((27*x+11)/16)/3)). - Vladimir Kruchinin, Mar 25 2019
a(n) = (1/n)*Sum_{m=1..n} m*Sum_{k=0..n-m} C(k,n-m-k)*C(n+k-1,k), n>0, a(0)=1. - Vladimir Kruchinin, Mar 26 2019
a(n) ~ 3^(3*n + 1/2) / (2^(7/2) * sqrt(Pi) * n^(3/2) * 5^(n - 1/2)). - Vaclav Kotesovec, Oct 07 2021
Conjecture: a(n) = (v_n + v_{n+1})/2 for n > 0 with a(0) = 1 where we start with vector v of fixed length m with elements v_i = 1 and for i=1..m-2, for j=i+2..m apply v_j := Sum_{k=0..2} v_{j-k}. - Mikhail Kurkov, Sep 03 2024

a(10)-a(25) from Alois P. Heinz, Feb 22 2017

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A263778 Number of inversion sequences avoiding pattern 120.

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A263779 Number of inversion sequences avoiding pattern 010.

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A263780 Number of inversion sequences avoiding pattern 100.

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A279570 Number of length n inversion sequences avoiding the patterns 110 and 120.

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A279559 Number of length n inversion sequences avoiding the patterns 010 and 120.

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A279555 Number of length n inversion sequences avoiding the patterns 110, 210, 120, and 010.

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A279564 Number of length n inversion sequences avoiding the patterns 000 and 100.

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A279566 Number of length n inversion sequences avoiding the patterns 102 and 201.

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A279557 Number of length n inversion sequences avoiding the patterns 110, 120, and 021.

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