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.

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

Author

Andrew Howroyd, Sep 12 2019

Keywords

• nonn

Examples

			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
		

Crossrefs

Cf. A283117, A289709.

Programs

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

Extensions

More terms from Bert Dobbelaere, May 14 2021