A334004 Number of spanning trees in the graph P_9 x P_n.

1, 40545, 750331584, 11905151192865, 179796299139278305, 2662079368040434932480, 39067130344394503972142977, 570929651486775190858844600865, 8326627661691818545121844900397056, 121316352059447360262303173959408358625, 1766658737971934774798769007686932254154689

Offset: 1

Author

Seiichi Manyama, Apr 12 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, order 256.

Crossrefs

Row m=9 of A116469.

Programs

Mathematica

a[n_] := Resultant[ChebyshevU[n - 1, x/2], ChebyshevU[8, (4 - x)/2], x]; Array[a, 11] (* Amiram Eldar, May 04 2021 *)

PARI

{a(n) = polresultant(polchebyshev(n-1, 2, x/2), polchebyshev(8, 2, (4-x)/2))}

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A116469(n, k):
    if n == 1 or k == 1: return 1
    universe = tl.grid(n - 1, k - 1)
    GraphSet.set_universe(universe)
    spanning_trees = GraphSet.trees(is_spanning=True)
    return spanning_trees.len()
def A334004(n):
    return A116469(n, 9)
print([A334004(n) for n in range(1, 10)])