A Survey on Triangular Number, Factorial and Some Associated Numbers

Castillo, Romer C.

doi:10.17485/ijst/2016/v9i41/85182

Cited by 5 publications

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“…In the past sections, we have discussed and discussed some mathematical and numerical properties about 2D figurate numbers and 3D figurate numbers (Castillo, 2016). We show.…”

Section: Resultsmentioning

confidence: 94%

Plane and Space figurate numbers: visualization with the GeoGebra´s help

Alves¹,

Barros²

2019

ADN

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The study and interest of figurate numbers can be observed even in ancient Greece. On the other hand, it becomes very important the historical understanding about an evolutionary process and the particular generalization of such 2D, 3D and m-D figurate numbers and they remain the interest of current scientific investigations. On the other hand, in Brazil, when we talk about Mathematics Education, the component of visualization acquires more and more relevance for the teaching. In this way, in the present work, we present a proposal of discussion of the figure numbers, with idea that the understanding of arithmetic, algebraic and geometric properties can be facilitated with the use of GeoGebra software and it´s use by the mathematical teacher.

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“…In the past sections, we have discussed and discussed some mathematical and numerical properties about 2D figurate numbers and 3D figurate numbers (Castillo, 2016). We show.…”

Section: Resultsmentioning

confidence: 94%

Plane and Space figurate numbers: visualization with the GeoGebra´s help

Alves¹,

Barros²

2019

ADN

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“…The first few triangular numbers are: (sequence A000217 in the OEIS). Oblong and triangular sequences have been studied by many authors and more detail can be found in the extensive literature dedicated to these sequences, see for example, [2,5,8,10,11,12,14,26,29] and references therein. For more references, see the sequences A002378 and A000217 in the OEIS.…”

Section: Yüksel Soykanmentioning

confidence: 99%

“…The study of these numbers dates back to Aristotle. The first few oblong numbers are: 0, 2,6,12,20,30,42,56,72,90,110,132,156,182,210,240,272,306,342,380, 420, 462, . .…”

Section: Introductionmentioning

confidence: 99%

Generalized Guglielmo Numbers: An Investigation of Properties of Triangular, Oblong and Pentagonal Numbers via Their Third Order Linear Recurrence Relations

Soykan

2022

EJMS

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“…Studies on factorials, triangular numbers, and other numbers associated with them abound the literature and have a long history of research in number theory. A survey on factorials, triangular numbers, and factoriangular numbers is provided in a recent article [1]. While factorials and triangular numbers have long been studied,…”

Section: Introductionmentioning

confidence: 99%

On the Generalization of Factoriangular Numbers

Castillo

2022

ARJOM

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A factoriangular number is a sum of a factorial and its corresponding triangular number. This paper presents some forms of the generalization of factoriangular numbers. One generalization is the \(n^{(m)}\) -factoriangular number which is of the form \((n!)^{m}\) + \(S_m(n)\), where \((n!)^{m}\) is the \(m\)th power of the factorial of \(n\) and \(S_m(n)\) is the sum of the \(m\)-powers of \(n\). This generalized form is explored for the different values of the natural number \(m\). The investigation results to some interesting proofs of theorems related thereto. Two important formulas were generated for \((n)^{m}\) -factoriangular number: \(Ft_{n^{(m)}}\) = \(Ft_{n^{(2k)}}\) = \((n!)^{2k}\) + \(2n+1\over2k+1\)\([n^{2k-2}+P(n^{2k-3})]T_n\) for even \(m=2k\), and \(Ft_{n^{(m)}}\) = \(Ft_{n^{(2k+1)}}\) = \((n!)^{2k+1}\) + \(n(n+1)\over k+1\)\([n^{2k-2}+P(n^{2k-3})]T_n\) for odd \(m=2k+1\)

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A Survey on Triangular Number, Factorial and Some Associated Numbers

Cited by 5 publications

References 0 publications

Plane and Space figurate numbers: visualization with the GeoGebra´s help

Plane and Space figurate numbers: visualization with the GeoGebra´s help

Generalized Guglielmo Numbers: An Investigation of Properties of Triangular, Oblong and Pentagonal Numbers via Their Third Order Linear Recurrence Relations

On the Generalization of Factoriangular Numbers

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