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

1,1

Links

Table of n, a(n) for n=1..42.

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

Cf. A283117, A289709.

Sequence in context: A357320 A174455 A245596 * A083293 A350912 A055370

Adjacent sequences: A326608 A326609 A326610 * A326612 A326613 A326614

Keyword

nonn

Author

Andrew Howroyd, Sep 12 2019

Extensions

More terms from Bert Dobbelaere, May 14 2021

Status

approved