A357596 Number of marked chord diagrams (linear words in which each letter appears twice) with n chords, whose intersection graph is distance-hereditary.

1, 1, 3, 15, 105, 923, 9417, 105815, 1267681, 15875631, 205301361

Offset

0,3

Comments

For n < 5, all intersection graphs on n vertices are distance-hereditary, so the first 4 terms coincide with the number of linear chord diagrams (given by the double factorial numbers; see A001147).

Links

Table of n, a(n) for n=0..10.

Christopher-Lloyd Simon, Topologie et dénombrement des courbes algébriques réelles, arXiv:2106.15450 [math.AG], 2021.

Christopher-Lloyd Simon, Topologie et dénombrement des courbes algébriques réelles, Annales de la faculté des sciences de Toulouse : Mathématiques, 6e série, 31(2): 383--422, 2022.

Formula

G.f. is algebraic: (z^3 + z^2)*A^6 - z^2*A^5 - 4*z*A^4 + (8*z + 2)*A^3 - (4*z + 6)*A^2 + 6*A - 2 = 0.

Crossrefs

Cf. A277862, A277869, A354588.

Sequence in context: A015682 A291744 A246860 * A249014 A258498 A189919

Adjacent sequences: A357593 A357594 A357595 * A357597 A357598 A357599

Keyword

nonn,more

Author

Christopher-Lloyd Simon, Oct 05 2022

Status

approved