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.

User: Mitchel T. Keller

Mitchel T. Keller's wiki page.

Mitchel T. Keller has authored 3 sequences.

A293501 Number of unlabeled semiorders on n points and having dimension 3.

Original entry on oeis.org

3, 40, 318, 1974, 10603, 51894, 238413, 1047440, 4454826, 18496217, 75416600, 303287250, 1206781482, 4762466651, 18674965709, 72866587238, 283217927396, 1097537249485, 4243554109115, 16379413110981, 63142882465324, 243203630272390
Offset: 7

Author

Mitchel T. Keller, Oct 10 2017

Keywords

Crossrefs

Formula

a(n) = A000108(n) - A293498(n).

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

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).

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) ).

A293498 Number of unlabeled semiorders on n points and having dimension at most 2.

Original entry on oeis.org

1, 2, 5, 14, 42, 132, 426, 1390, 4544, 14822, 48183, 156118, 504487, 1627000, 5240019, 16861453, 54228190, 174351450, 560481708, 1801653769, 5791301311, 18615976402, 59841686254, 192366897839, 618392292337
Offset: 1

Author

Mitchel T. Keller, Oct 10 2017

Keywords

Formula

G.f.: -x*(5*x^7 - 41*x^6 + 101*x^5 - 129*x^4 + 96*x^3 - 42*x^2 + 10*x - 1)/(7*x^8 - 66*x^7 + 197*x^6 - 311*x^5 + 294*x^4 - 172*x^3 + 61*x^2 - 12*x + 1).