Let $\textbf{C}/C$ be a slice category with base object $C$.
The functor that comes to mind is the one such that objects $f:X \to C$ are mapped to $X$, and arrows $a: X \to X'$ are mapped to themselves.
Let $F$ be this mapping. Then since, the identiy on the object $f: X\to C$, is $1_X$, we ha...
@MartinSleziak I have at least created the very basic tag-excerpt and tag-wiki for sierpinski-numbers. And I will remove the tag from the two questions which seem to be about Sirepinski triangle rather than about Sirepinski numbers.
About Sierpinski triangles: Express the areas of the shaded triangles in the $n$th stage as a sum of a geometric series.
How do I represent the increasing triangles as a partial sum of a geometric series?
Sierpinski triangles: The Sierpinski triangle iterates an equilateral triangle (stage 0) b...
We have
$f(0) = 1 , f(1) = 4 , f(2) = 13 , f(n) = f(n-1) + 3^n$
(number of all of triangles in Sierpinski triangle)
I want to find a non recursive function.
I know the answer but I want a solution for it.
Let $\textbf{C}/C$ be a slice category with base object $C$.
The functor that comes to mind is the one such that objects $f:X \to C$ are mapped to $X$, and arrows $a: X \to X'$ are mapped to themselves.
Let $F$ be this mapping. Then since, the identiy on the object $f: X\to C$, is $1_X$, we ha...
We have
$f(0) = 1 , f(1) = 4 , f(2) = 13 , f(n) = f(n-1) + 3^n$
(number of all of triangles in Sierpinski triangle)
I want to find a non recursive function.
I know the answer but I want a solution for it.
