A334002 Number of spanning trees in the graph P_7 x P_n.

1, 2911, 4768673, 7022359583, 10021992194369, 14143261515284447, 19872369301840986112, 27873182693625548898079, 39067130344394503972142977, 54740416599810921320592441119, 76692291658239649098972455530913, 107441842254735898225957962027174559, 150517199699838971875005120330439121217

Offset: 1

Author

Seiichi Manyama, Apr 12 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..200
• Vaclav Kotesovec, Generating function
• Index entries for linear recurrences with constant coefficients, order 48.

Crossrefs

Row m=7 of A116469.

Programs

Mathematica

a[n_] := Resultant[ChebyshevU[n - 1, x/2], ChebyshevU[6, (4 - x)/2], x]; Array[a, 13] (* Amiram Eldar, May 04 2021 *)

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 A334002(n):
    return A116469(n, 7)
print([A334002(n) for n in range(1, 15)])