# Recurrence Relationship Help Request

I have been playing with the recurrence relation

$p_n = np_{n-1} + p_{n-2}$ such that $$p_0 = 0 , p_1 = 1$$.

I have found a few interesting difference forms for it but no closed form formula. Can anyone find a nice closed form formula, generating function or interpretation for what this might count.

All thoughts appreciated and welcome :)

Note by Roberto Nicolaides
1 year, 3 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

## Comments

Sort by:

Top Newest

Whenever you're investigating a sequence, it's not a bad idea to check the OEIS. This is entry A001053. There doesn't seem to be too much information.

- 1 year, 3 months ago

Log in to reply

Thanks Jon, this is a nice idea :) I did have a quick look and agreed that there was not a lot of info! I will be having a look at bessel funtions soon to try get more intuition on the problem :)

- 1 year, 3 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...