A321740 Number of representations of n as a truncated triangular number.

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, 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, 1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0

Offset

1,36

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. This sequence gives the number of ways that a number can be represented in this form.

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

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.

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

Links

Table of n, a(n) for n=1..92.

Example

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).

Crossrefs

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

Sequence in context: A010108 A033782 A302721 * A098082 A321921 A236419

Adjacent sequences: A321737 A321738 A321739 * A321741 A321742 A321743

Keyword

nonn

Author

Allan C. Wechsler, Nov 17 2018

Extensions

More terms from Hugo Pfoertner, Sep 18 2020

Status

approved