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 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 (list; graph; refs; listen; history; text; internal format)
 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 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. LINKS Table of n, a(n) for n=1..53. 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). Sequence in context: A025399 A171390 A034813 * A262796 A255101 A255094 Adjacent sequences: A319599 A319600 A319601 * A319603 A319604 A319605 KEYWORD easy,nonn AUTHOR Allan C. Wechsler, Nov 15 2018 EXTENSIONS More terms from Alois P. Heinz, Nov 15 2018 STATUS approved

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Last modified March 3 10:32 EST 2024. Contains 370510 sequences. (Running on oeis4.)