

A319602


Numbers with at least two representations as truncated triangular numbers.


3



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

1,1


COMMENTS

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 sidelength pairs that give the same count.
The underlying quadratic form is (4ab + a(a3) + b(b3) + 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.


LINKS



EXAMPLE

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)


CROSSREFS

Cf. A008912 (all truncated triangular numbers), A008867 (see comments).


KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



