Tagged Questions

0
votes
0answers
41 views

Combinatorial Recursion 2

Define a recursion $a(n,k)$ that gives the number of ways to choose $n$ items out of $k$ types of items, with the condition that we must choose $2, 4$, or $6$ items of each type. So $2p+4q+6r = n$ ...
0
votes
1answer
50 views

Combinatorial Recursion

Define a recursion that gives the number of sequences that include the numbers $0,1,2,3$ with an even number of $1$'s and an even number of $0$'s. So far I got $$a(n) = 2a(n-1) + 2a(n-2)$$ which ...
3
votes
1answer
57 views

Give a combinatorial proof of the recurrence relation

Let $F_n$ be the number of forests on the vertex set $V = \{1,2,\ldots,n\}$(Thus we are counting labelled forests). Give a combinatorial proof of the recurrence relation $$F_n = \sum_{i=1} ...
1
vote
2answers
58 views

Guidelines for Obtaining Recursive Equations?

I'm trying to teach myself some combinatorics, and at the moment, I'm having a hard time coming up with recursive equations. It seems to come naturally to some people, and I'm hoping that my skills ...
1
vote
2answers
32 views

Simple linear recursion

$x_n=\frac{x_{n-1}}{a}+\frac{b}{a}$ with $a>1, b>0$ and $x_0>0$ I tried to solve it using the generating function but it does not work because of $\frac{b}{a}$, so may you have an idea.
2
votes
1answer
81 views

OEIS A000255 recursion.

I encountered the sequence A000255. $a(n)$ counts permutations of $[1,...,n+1]$ having no substring $[k,k+1]$ I am finding difficulty in proving it. Can you please give any clues or hints on how to ...
2
votes
2answers
106 views

Need to find the recurrence equation for coloring a 1 by n chessboard

So the question asks me to find the number of ways H[n] to color a 1 by n chessboard with 3 colors - red, blue and white such that the number of red squares is even and number of blue squares is at ...
7
votes
1answer
368 views

Bell numbers, recursions, bijections

The $n$th Bell number, named after Eric Temple Bell (although he was far from the first to think about them), is the number of partitions of a set of cardinality $n$. If they are written in the top ...