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A321443 Number of "bilaterally symmetric hexagonal partitions" of n 2
1, 1, 2, 2, 4, 2, 5, 3, 5, 4, 7, 2, 8, 4, 7, 5, 9, 2, 11, 5, 8, 5, 10, 4, 13, 6, 8, 5, 13, 4, 16, 4, 8, 8, 14, 5, 16, 5, 11, 7, 16, 2, 17, 9, 12, 8, 13, 4, 20, 8, 14, 7, 15, 5, 22, 7, 11, 8, 20, 4, 23, 8, 10, 11, 20, 7, 20, 4, 17, 9, 24, 5, 22, 7, 13, 13, 16 (list; graph; refs; listen; history; text; internal format)
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
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
A321441 counts hexagonal partitions in general. A321440 counts a different special kind of hexagonal partition. A116513 counts hexagonal "diagrams", of which these partitions are a sort of projection.
Sequence in context: A187782 A129296 A300837 * A333836 A125296 A366707
KEYWORD
nonn
AUTHOR
Allan C. Wechsler, Nov 09 2018
EXTENSIONS
More terms from Chai Wah Wu, Nov 10 2018
STATUS
approved

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Last modified March 19 02:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)