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A321443
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Number of "bilaterally symmetric hexagonal partitions" of n
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2
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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)
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PROG
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(Python)
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
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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