A322491 -id:A322491

Search: a322491 -id:a322491

Displaying 1-2 of 2 results found.

page 1

A321740

Number of representations of n as a truncated triangular number.

+10
2

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

(list; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn

AUTHOR

Allan C. Wechsler, Nov 17 2018

EXTENSIONS

More terms from Hugo Pfoertner, Sep 18 2020

STATUS

approved

A322492

Records in the number of ways to represent a number as truncated triangular number A008912.

+10
2

1, 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 108, 128, 144, 192

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The numbers where the record is first achieved are provided as A322491.

LINKS

Table of n, a(n) for n=1..19.

PROG

(PARI) v=vectorsmall(20000000); for(n=1, 5100, for(k=1, n-1, my(t=n*(n-3)/2-k^2+k*n+1); v[t]++)); vm=0; for(k=1, #v, if(v[k]>vm, print1(v[k], ", "); vm=v[k])) \\ Hugo Pfoertner, Sep 18 2020

CROSSREFS

Cf. A008867, A008912, A319602, A321740, A322491.

KEYWORD

nonn,more

AUTHOR

Hugo Pfoertner, Dec 12 2018

STATUS

approved

page 1

Search completed in 0.007 seconds