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A319602 Numbers with at least two representations as truncated triangular numbers.

%I A319602 #39 Dec 12 2018 14:27:41
%S A319602 36,75,91,102,127,153,168,190,192,201,213,231,267,270,300,322,333,348,
%T A319602 351,361,388,397,420,426,432,435,465,487,498,531,543,546,558,582,586,
%U A319602 595,621,627,630,657,663,673,685,696,712,717,738,762,768,777,811,816,817
%N A319602 Numbers with at least two representations as truncated triangular numbers.
%C A319602 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.
%C A319602 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.)
%C A319602 A number occurs at least three times in A008867 if and only if it occurs in this sequence.
%e A319602 75 is in the list because there are 75 dots in both the (2,10) hexagon and the (5,6) hexagon.
%e A319602 Table of solutions for the smallest 10 examples:
%e A319602 36: (1,8) (3,5)
%e A319602 75: (2,10) (5,6)
%e A319602 91: (1,13) (6,6)
%e A319602 102: (2,12) (4,9)
%e A319602 127: (3,12) (7,7)
%e A319602 153: (1,17) (4,12)
%e A319602 168: (2,16) (7,9)
%e A319602 190: (1,19) (7,10)
%e A319602 192: (4,14) (8,9)
%e A319602 201: (3,16) (5,13)
%Y A319602 Cf. A008912 (all truncated triangular numbers), A008867 (see comments).
%K A319602 easy,nonn
%O A319602 1,1
%A A319602 _Allan C. Wechsler_, Nov 15 2018
%E A319602 More terms from _Alois P. Heinz_, Nov 15 2018