cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Allan C. Wechsler, Nov 17 2018

Keywords

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.

Examples

			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.

Extensions

More terms from Hugo Pfoertner, Sep 18 2020

A322491 Numbers representable as truncated triangular numbers A008912 in more ways than any smaller number.

Original entry on oeis.org

1, 3, 36, 465, 1323, 9045, 38646, 117582, 334656, 1429893, 4350525, 18588606, 87223458, 265382010, 928000395, 4702917255, 5989820730, 12064005132, 56608024080
Offset: 1

Views

Author

Hugo Pfoertner, Dec 12 2018

Keywords

Comments

The corresponding numbers of representations are provided as A322492.

Examples

			a(2) = 3 because 3 is the least number occurring more than 1 time in A008867.
a(3) = 36 because 36 is the first number occurring more often (A322492(2) = 4 times) than a(2) = 3 and all numbers < 36 in A008867.

Crossrefs

Cf. A008867, A008912, A319602, A321740.
Showing 1-2 of 2 results.

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