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A319602
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Numbers with at least two representations as truncated triangular numbers.
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3
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36, 75, 91, 102, 127, 153, 168, 190, 192, 201, 213, 231, 267, 270, 300, 322, 333, 348, 351, 361, 388, 397, 420, 426, 432, 435, 465, 487, 498, 531, 543, 546, 558, 582, 586, 595, 621, 627, 630, 657, 663, 673, 685, 696, 712, 717, 738, 762, 768, 777, 811, 816, 817
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OFFSET
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1,1
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COMMENTS
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A truncated triangular number is a figurate number, the number of dots in a hexagonal diagram where the side lengths alternate between two values. Include a number in this list if there are two different side-length pairs that give the same count.
The underlying quadratic form is (4ab + a(a-3) + b(b-3) + 2)/2; n is in the list if n can be expressed in this form in two different ways, where a <= b. (That is, exchanging a and b is not considered different.)
A number occurs at least three times in A008867 if and only if it occurs in this sequence.
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LINKS
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EXAMPLE
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75 is in the list because there are 75 dots in both the (2,10) hexagon and the (5,6) hexagon.
Table of solutions for the smallest 10 examples:
36: (1,8) (3,5)
75: (2,10) (5,6)
91: (1,13) (6,6)
102: (2,12) (4,9)
127: (3,12) (7,7)
153: (1,17) (4,12)
168: (2,16) (7,9)
190: (1,19) (7,10)
192: (4,14) (8,9)
201: (3,16) (5,13)
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CROSSREFS
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Cf. A008912 (all truncated triangular numbers), A008867 (see comments).
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KEYWORD
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easy,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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