Romer C. Castillo (M.Sc.)
Batangas State University, Batangas City, Philippines
romercastillo@rocketmail.com
Date Received: August 3, 2015; Date Revised: September 18, 2015
Asia Pacific Journal of Multidisciplinary Research
Vol. 3 No. 4, 95-101
November 2015 Part II
P-ISSN 2350-7756
E-ISSN 2350-8442
On the Sum of Corresponding Factorials and Triangular Numbers: Runsums, Trapezoids and Politeness 582 KB 1 downloads
Romer C. Castillo (M.Sc.) Batangas State University, Batangas City, Philippines romercastillo@rocketmail.com Date...
When corresponding numbers in the sequence of factorials and sequence of triangular numbers are added, a new sequence of natural numbers is formed. In this study, these positive integers are called factoriangular numbers. Closely related to these new numbers are the runsums, trapezoidal and polite numbers. Some theorems on runsum representations of factoriangular numbers are proven here, as well as, a theorem on factoriangular number being represented as difference of two triangular numbers. Unambiguous definitions of trapezoidal number and number of trapezoidal arrangements are also given, including how these differ from runsum, polite number, number of runsums and politeness.
Keywords – factoriangular number, polite number, runsum, trapezoidal arrangement, trapezoidal number