OFFSET
0,5
FORMULA
a(n) >= A362144(n)/4.
PROG
(Python)
from math import comb
def F(i, j, k):
# total number of tilings using i, j, and 2*j+3*k squares of side lengths 3, 2, and 1, respectively
return comb(i+j+k, i)*comb(j+k, j)*2**j
def F0(i, j, k):
# number of inequivalent tilings
x = F(i, j, k)
if j == 0: x += comb(i+k, i) # horizontal line of symmetry
if i%2+j%2+k%2 <= 1: x += 2*F(i//2, j//2, k//2) # vertical line of symmetry or rotational symmetry
return x//4
def A362261(n):
return max(F0(i, j, n-3*i-2*j) for i in range(n//3+1) for j in range((n-3*i)//2+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Pontus von Brömssen, Apr 15 2023
STATUS
approved