cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 41-43 of 43 results.

A336072 Number of inversion sequences avoiding the vincular pattern 2-01 (or 2-10).

Original entry on oeis.org

1, 2, 6, 24, 118, 680, 4460, 32634, 262536, 2296532
Offset: 1

Views

Author

Michael De Vlieger, Jul 07 2020

Keywords

Links

Crossrefs

Cf. A000079, A000110, A022493, A091768, A102038, A113227, A263777, A328441, A336070, A336071.

A293499 Number of unlabeled hereditary semiorders on n points.

Original entry on oeis.org

1, 2, 5, 14, 42, 132, 428, 1415, 4730, 15901, 53593, 180809, 610157, 2058962, 6947145, 23437854, 79067006, 266717300, 899693960, 3034814143, 10236853534, 34530252629, 116475001757, 392885252033
Offset: 1

Views

Author

Mitchel T. Keller, Oct 10 2017

Keywords

Comments

A semiorder (poset avoiding the subposets 2+2 and 1+3, or an interval order having a representation in which all intervals have the same length) is hereditary if every initial subsequence of the ascent sequence associated to the semiorder by the bijection of Bousquet-Mélou et al. corresponds to a semiorder.

References

  • M. T. Keller and S. J. Young, Hereditary semiorders and enumeration of semiorders by dimension. Preprint (2017).

Links

Crossrefs

Cf. A022493.

Programs

  • Mathematica
    CoefficientList[ Series[(-1 +6x -12x^2 +9x^3 -x^4)/(-1 +8x -23x^2 +29x^3 -14x^4 +x^5), {x, 0, 26}], x] (* or *)
LinearRecurrence[{8, -23, 29, -14, 1}, {1, 2, 5, 14, 42}, 27] (* Robert G. Wilson v, Jan 07 2018 *)

Formula

G.f.: -x*(1 - 6*x + 12*x^2 - 9*x^3 + x^4) / ( (x-1)*(x^4 - 13*x^3 + 16*x^2 - 7*x + 1) ).

A368636 Number of modified ascent sequences of length n avoiding the pattern 221.

Original entry on oeis.org

1, 1, 2, 5, 14, 44, 155, 607, 2617, 12306, 62587, 341790, 1991916, 12324031, 80587935, 554826429, 4008364544, 30299290911, 239019427636, 1963239741712, 16755637216417, 148317595764043, 1359380603278377, 12880841117125364, 126007744452786277, 1270998629233371388
Offset: 0

Views

Author

Giulio Cerbai, Jan 19 2024

Keywords

Examples

			The shortest modified ascent sequence that contains 221 is 1221.

Links

Crossrefs

Cf. A022493 (all modified ascents).

Programs

  • Mathematica
    a[0]=1; a[n_]:=Sum[Sum[StirlingS2[k-1,i-1] Binomial[n-1-k+i,i-1],{i,k}],{k,n}]; Array[a,26,0] (* Stefano Spezia, Jan 20 2024 *)

Formula

a(n) = Sum_{k=1..n} Sum_{i=1..k} S2(k-1,i-1) * binomial(n-1-k+i,i-1) for n >= 1, a(0)=1, where S2(n,i) are the Stirling numbers of the second kind.
Previous Showing 41-43 of 43 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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