pentagonalrekurs
Pentagonalrekurs, or pentagonal recursion, is a term used in some mathematical discussions to denote a family of recursive schemes whose increments are governed by pentagonal-number patterns. In its simplest instantiation, it defines a sequence by a(0)=0 and a(n)=a(n-1) + 3n - 2 for n≥1. This yields the pentagonal numbers P(n) = n(3n-1)/2, with initial values 0, 1, 5, 12, 22, 35, etc.
Variants of pentagonalrekurs appear in related areas such as partition theory and polygonal number sequences. A
The concept is connected to broader ideas in number theory and combinatorics, including Euler’s pentagonal number
See also: pentagonal numbers, Euler’s pentagonal number theorem, polygonal numbers, recurrence relations.