A330966 a(n) is 1/5 times the number of anti-chains of size four in "0,1,2" Motzkin trees on n edges.

1, 11, 84, 520, 2835, 14133, 65960, 292536, 1245789, 5132375, 20569512, 80541300, 309143065, 1166302239, 4334300976, 15895046840, 57608669274, 206606077758, 733992204988, 2585415612500, 9036556157100, 31362262768684, 108144498780096, 370700681812032

Offset: 6

Author

Petros Hadjicostas, Jun 08 2020

Keywords

• nonn

Comments

See A335355 for details.

Links

• Lifoma Salaam, Combinatorial statistics on phylogenetic trees, Ph.D. Dissertation, Howard University, Washington D.C., 2008; see Definition 42 (p. 30), Theorem 44 (p. 33), and Table 2.4 (p. 39).

Crossrefs

Cf. A001006, A002426, A335355.

Programs

PARI

default(seriesprecision, 50);
M(z) = (1 - z - sqrt(1 - 2*z - 3*z^2))/(2*z^2); /* g.f. of A001006 */
T(z) = 1/sqrt(1 - 2*z - 3*z^2); /* g.f. of A002426 */
for(n=0, 30, print1(polcoef(z^6*T(z)^7*M(z)^4, n, z), ", "))

Formula

a(n) = A335355(n)/5.

D-finite with recurrence -(n+2)*(n-6)*a(n) +(n+2)*(4*n-17)*a(n-1) +(2*n^2-n-90)*a(n-2) -3*(n+2)*(4*n-3)*a(n-3) -9*(n+2)*(n+1)*a(n-4)=0. - R. J. Mathar, Aug 19 2022