OFFSET
0,3
COMMENTS
A bilaterally symmetric hexagonal partition is one whose parts are consecutive integers, of which all have multiplicity 2 except the largest part, which may have any multiplicity (including 1).
This is a restriction of the concept of hexagonal partition presented in A321441. The nomenclature is suggested by presenting such partitions as hexagonal patches of the triangular lattice A2.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..10000
EXAMPLE
Here are the derivations of the terms up through n = 10. Partitions are abbreviated as strings of digits.
n = 0: (empty partition)
n = 1: 1
n = 2: 11, 2
n = 3: 111, 3
n = 4: 1111, 112, 22, 4
n = 5: 11111, 5
n = 6: 111111, 1122, 222, 33, 6
n = 7: 1111111, 223, 7
n = 8: 11111111, 11222, 2222, 44, 8
n = 9: 111111111, 11223, 333, 9
n = 10: 1111111111, 112222, 22222, 2233, 334, 55, (10)
PROG
(Python)
def A321443(n):
if n == 0:
return 1
c = 0
for i in range(n):
mi = i*(i+1) + n
for j in range(i+1, n+1):
k = mi - j*j
if k < 0:
break
if not k % j:
c += 1
return c # Chai Wah Wu, Nov 10 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Allan C. Wechsler, Nov 09 2018
EXTENSIONS
More terms from Chai Wah Wu, Nov 10 2018
STATUS
approved