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A326611
Number of arrangements of rooks with rotational symmetry on a triangular grid with n grid points on each side and no two rooks on the same row, column or diagonal.
4
2, 1, 1, 4, 3, 5, 10, 9, 15, 40, 41, 65, 162, 189, 321, 780, 919, 1681, 4034, 5281, 9259, 23936, 30665, 57601, 143602, 199577, 367561, 959236, 1323243, 2585133, 6580650, 9609145, 18433799, 49030248, 71211721, 142636377, 371147842, 566921925, 1122881889, 3024341084, 4583822647, 9446124313
OFFSET
1,1
EXAMPLE
The four cases for n = 4 are:
o o o o
o o o o X o o X
o o o o X o o o X X o o
o o o o o o o o o X o o o o X o
PROG
(Python)
def solve(cli):
count = 1
for k in range(len(cli)):
x, y, z = cli[k]
clo = []
for c in cli[k+1:]:
if (not x in c) and (not y in c) and (not z in c):
clo.append(c)
count += 2*solve(clo)
return count
def A326611(n):
c0 = []
for x in range(n):
for y in range(x+1, n):
z = n-1-x-y
if z>y: c0.append((x, y, z))
count = solve(c0)
if n%3 == 1:
c1 = [c for c in c0 if not n//3 in c]
count += solve(c1)
return count
# Bert Dobbelaere, May 14 2021
CROSSREFS
Sequence in context: A357320 A174455 A245596 * A083293 A350912 A055370
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Sep 12 2019
EXTENSIONS
More terms from Bert Dobbelaere, May 14 2021
STATUS
approved