OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Spanning Tree
FORMULA
Empirical g.f.: x*(-15*x^3 - 111*x^2 + 97*x + 1) / (x^4 - 95*x^3 + 384*x^2 - 95*x + 1). - Vaclav Kotesovec, Dec 04 2020
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_nXk_king_graph(n, k):
grids = []
for i in range(1, k + 1):
for j in range(1, n):
grids.append((i + (j - 1) * k, i + j * k))
if i < k:
grids.append((i + (j - 1) * k, i + j * k + 1))
if i > 1:
grids.append((i + (j - 1) * k, i + j * k - 1))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
return grids
def A338029(n, k):
if n == 1 or k == 1: return 1
universe = make_nXk_king_graph(n, k)
GraphSet.set_universe(universe)
spanning_trees = GraphSet.trees(is_spanning=True)
return spanning_trees.len()
def A338532(n):
return A338029(n, 3)
print([A338532(n) for n in range(1, 20)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 29 2020
STATUS
approved