A354588 Number of marked chord diagrams (linear words in which each letter appears twice) with n chords, whose intersection graph is connected and distance-hereditary.

1, 4, 27, 226, 2116, 21218, 222851, 2420134, 26954622, 306203536, 3534170486, 41326973520, 488562349730, 5829471835390, 70112478797987, 849110215237094, 10345827793291654, 126734013316914248, 1559884942820510474, 19281814963272771308, 239263099541276559360, 2979328903819471935332

Offset

0,2

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 with connected intersection graph.

Links

Table of n, a(n) for n=0..21.

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

a(n) = (1/(n+1))*Sum_{k=0..n} binomial(n+k, n)*binomial(2*(n+1)+k, n-k)*2^k.

G.f. satisfies C = z + 2*z*C + (z+2)*C^2 + 2*C^3.

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+k, n)*binomial(2*(n+1)+k, n-k)*2^k)/(n+1); \\ Michel Marcus, Oct 05 2022

Crossrefs

Cf. A277862, A277869, A357596.

Sequence in context: A365753 A317103 A341962 * A276029 A160883 A362274

Adjacent sequences: A354585 A354586 A354587 * A354589 A354590 A354591

Keyword

nonn

Author

Christopher-Lloyd Simon, May 31 2022

Status

approved