A202062
Number of ascent sequences avoiding the pattern 201.
Original entry on oeis.org
1, 1, 2, 5, 15, 52, 201, 843, 3764, 17659, 86245, 435492, 2261769, 12033165, 65369590, 361661809, 2033429427, 11597912588, 67004252081, 391599609911, 2312726369640, 13789161819383, 82932744795049, 502777950712812, 3070529443569777, 18879637374473465, 116815588935673706, 727011479685559453
Offset: 0
- Andrew Conway and Miles Conway, Table of n, a(n) for n = 0..133
- Giulio Cerbai, Modified ascent sequences and Bell numbers, arXiv:2305.10820 [math.CO], 2023. See p. 27.
- Giulio Cerbai, Anders Claesson and Luca Ferrari, Stack sorting with restricted stacks, arXiv:1907.08142 [cs.DS], 2019.
- Andrew R. Conway, Miles Conway, Andrew Elvey Price and Anthony J. Guttmann, Pattern-avoiding ascent sequences of length 3, arXiv:2111.01279 [math.CO], Nov 01 2021.
- P. Duncan and Einar Steingrimsson, Pattern avoidance in ascent sequences, arXiv preprint arXiv:1109.3641 [math.CO], 2011.
- Anthony Guttmann and Vaclav Kotesovec, L-convex polyominoes and 201-avoiding ascent sequences, arXiv:2109.09928 [math.CO], 2021.
Total number of ascent sequences is given by
A022493.
A202059
Number of ascent sequences avoiding the pattern 100.
Original entry on oeis.org
1, 1, 2, 5, 14, 44, 153, 583, 2410, 10721, 50965, 257393, 1374187, 7722862, 45520064, 280502924, 1802060232, 12040040899, 83475921469, 599400745354, 4449689901306, 34096169966924, 269286884243138, 2189193150557825, 18297258191472880, 157049750065028868
Offset: 0
- Andrew Conway and Miles Conway, Table of n, a(n) for n = 0..628
- Andrew R. Conway, Miles Conway, Andrew Elvey Price and Anthony J. Guttmann, Pattern-avoiding ascent sequences of length 3, arXiv:2111.01279 [math.CO], Nov 01 2021.
- P. Duncan and Einar Steingrimsson, Pattern avoidance in ascent sequences, arXiv preprint arXiv:1109.3641, 2011
Corrected a(7), was 383, but should be 583 according to Duncan-Steimgrimsson paper and independent computation. -
Andrew Baxter, Jan 06 2014
A202060
Number of ascent sequences avoiding the pattern 110.
Original entry on oeis.org
1, 1, 2, 5, 14, 43, 143, 510, 1936, 7774, 32848, 145398, 671641, 3227218, 16084747, 82955090, 441773793, 2424845273, 13695855478, 79485625385, 473393639992, 2889930405750, 18064609329598, 115513453404597, 754956282308784, 5039064184597772, 34323984497482559
Offset: 0
- Andrew Conway and Miles Conway, Table of n, a(n) for n = 0..43
- Andrew R. Conway, Miles Conway, Andrew Elvey Price and Anthony J. Guttmann, Pattern-avoiding ascent sequences of length 3, arXiv:2111.01279 [math.CO], Nov 01 2021.
- P. Duncan and Einar Steingrimsson, Pattern avoidance in ascent sequences, arXiv preprint arXiv:1109.3641, 2011
A202061
Number of ascent sequences avoiding the pattern 120.
Original entry on oeis.org
1, 1, 2, 5, 14, 42, 133, 442, 1535, 5546, 20754, 80113, 317875, 1292648, 5374073, 22794182, 98462847, 432498659, 1929221610, 8728815103, 40017844229, 185727603829, 871897549029, 4137132922197, 19828476952117, 95934298966615, 468291607852143, 2305162065138433
Offset: 0
- Liang Chengwei, Shi Lecun and Cai Zhongyu, Table of n, a(n) for n = 0..500 (terms 0..74 from Andrew Conway and Miles Conway)
- Andrew R. Conway, Miles Conway, Andrew Elvey Price and Anthony J. Guttmann, Pattern-avoiding ascent sequences of length 3, arXiv:2111.01279 [math.CO], Nov 01 2021.
- Paul Duncan and Einar Steingrimsson, Pattern avoidance in ascent sequences, arXiv preprint arXiv:1109.3641 [math.CO], 2011.
A294220
Number A(n,k) of ascent sequences of length n where no letter multiplicity is larger than k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 4, 1, 0, 1, 1, 2, 5, 10, 1, 0, 1, 1, 2, 5, 14, 27, 1, 0, 1, 1, 2, 5, 15, 47, 83, 1, 0, 1, 1, 2, 5, 15, 52, 180, 277, 1, 0, 1, 1, 2, 5, 15, 53, 210, 773, 1015, 1, 0, 1, 1, 2, 5, 15, 53, 216, 964, 3701, 4007, 1, 0
Offset: 0
A(4,2) = 10: 0123, 0011, 0012, 0101, 0102, 0110, 0112, 0120, 0121, 0122.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 2, 2, 2, 2, 2, 2, ...
0, 1, 4, 5, 5, 5, 5, 5, 5, ...
0, 1, 10, 14, 15, 15, 15, 15, 15, ...
0, 1, 27, 47, 52, 53, 53, 53, 53, ...
0, 1, 83, 180, 210, 216, 217, 217, 217, ...
0, 1, 277, 773, 964, 1006, 1013, 1014, 1014, ...
0, 1, 1015, 3701, 4960, 5270, 5326, 5334, 5335, ...
-
b:= proc(n, i, t, p, k) option remember; `if`(n=0, 1,
add(`if`(coeff(p, x, j)=k, 0, b(n-1, j, t+
`if`(j>i, 1, 0), p+x^j, k)), j=1..t+1))
end:
A:= (n, k)-> b(n, 0$3, min(n, k)):
seq(seq(A(n, d-n), n=0..d), d=0..12);
-
b[n_, i_, t_, p_, k_] := b[n, i, t, p, k] = If[n == 0, 1, Sum[ If[ Coefficient[p, x, j] == k, 0, b[n-1, j, t + If[j>i, 1, 0], p + x^j, k]], {j, 1, t+1}]];
A[n_, k_] := b[n, 0, 0, 0, Min[n, k]];
Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 11}] // Flatten (* Jean-François Alcover, Aug 05 2018, translated from Maple *)
Showing 1-5 of 5 results.
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