OFFSET
1,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..50
FORMULA
Empirical g.f.: 3*x*(2 + 15*x - 53*x^2 + 89*x^3 - 37*x^4) / ((1 - x)^2 * (1 - 3*x)^2 * (1 - 6*x + 3*x^2)). - Vaclav Kotesovec, Dec 19 2020
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_CnXPk(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))
grids.append((i + (n - 1) * k, i))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
return grids
def A(start, goal, n, k):
universe = make_CnXPk(n, k)
GraphSet.set_universe(universe)
paths = GraphSet.paths(start, goal)
return paths.len()
def B(n, k):
m = k * n
s = 0
for i in range(1, m):
for j in range(i + 1, m + 1):
s += A(i, j, n, k)
return s
def A338709(n):
return B(3, n)
print([A338709(n) for n in range(1, 11)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 18 2020
STATUS
approved