Pascals Triangle Manipulation

• rbzima
In summary, The conversation is about the manipulation of Pascals Triangle and finding a way to represent its rows in terms of combinations. The person who initiated the conversation is working on a problem involving two people on a board and believes this concept may be helpful. They also mention a possible pattern in the sum of the rows and provide a link for further reference.
rbzima
Here is the manipulation of Pascals Triangle. I'm trying to figure out a way to represent these rows in terms of a combination. Check it out...

1
1 1
1 4 1
1 9 9 1
1 16 36 16 1
1 25 100 100 25 1
.
.
.

Why have you posed this?

(nCk)2

mathman said:
Why have you posed this?

(nCk)2

Is there any particular pattern also with the sum of the rows as well?

The reason is because it's part of a problem I'm working on regarding two people at opposite corners on a massive n by n board. On player can only move north and east, the other south and west. Basically, I need to find the expected value of the number of times they will meet, and I have a hunch this plays a part in. Thanks!

rbzima said:
Is there any particular pattern also with the sum of the rows as well?

See http://www.research.att.com/~njas/sequences/A000984" .

Last edited by a moderator:

What is Pascals Triangle Manipulation?

Pascals Triangle Manipulation is a mathematical concept that involves rearranging and manipulating the numbers in Pascals Triangle, a mathematical triangle named after French mathematician Blaise Pascal. It is a useful tool for solving various mathematical problems and patterns.

What is the purpose of Pascals Triangle Manipulation?

The purpose of Pascals Triangle Manipulation is to identify patterns and relationships between numbers in Pascals Triangle, and use them to solve mathematical problems. It can also be used to calculate various mathematical sequences, such as the Fibonacci sequence.

How is Pascals Triangle Manipulation performed?

Pascals Triangle Manipulation involves rearranging the numbers in Pascals Triangle in different ways, such as adding, subtracting, or multiplying them. This can be done manually or by using mathematical formulas and algorithms.

What are the applications of Pascals Triangle Manipulation?

Pascals Triangle Manipulation has various applications in mathematics, such as calculating binomial coefficients, solving probability problems, and finding patterns in number sequences. It is also used in computer science and coding for tasks such as image compression and error detection.

Are there any real-world examples of Pascals Triangle Manipulation?

Yes, Pascals Triangle Manipulation has many real-world applications. For example, it can be used to calculate the number of possible combinations in a lottery or to find the probability of winning a game. It is also used in genetics to predict the likelihood of certain traits being inherited from parents.

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