%I #14 Sep 19 2020 03:41:57

%S 1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0,1,0,

%T 0,2,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,0,0,

%U 1,0,0,0,1,0,2,0,0,1,0,0,0,1,0,0,0,0,1,1,0,1,2,0

%N Number of representations of n as a truncated triangular number.

%C A truncated triangular number is a figurate number, the number of dots in a hexagonal diagram where the side lengths alternate between two values. This sequence gives the number of ways that a number can be represented in this form.

%C In a sense this sequence is a hexagonal analog of A038548, which asks the same question for rectangular numbers, and A001227 for trapezoidal numbers.

%C These sequences usually turn out to count divisors of a particular form, of a number simply related to n, but such a formulation is not yet known in this case.

%C Indices for which this sequence is nonzero are at A008912; this sequence is 2 or greater at the indices given in A319602.

%e a(36) = 2 because 36 can be achieved with hexagons of sides (1,9,1,9,1,9) and (3,5,3,5,3,5).

%Y Cf. A008912, A008867, A319602, A322491, A322492.

%K nonn

%O 1,36

%A _Allan C. Wechsler_, Nov 17 2018

%E More terms from _Hugo Pfoertner_, Sep 18 2020