# Tagged Questions

1. From a samples of a small samples of mathematical objects, conjecture a common pattern to all of them. This includes "guess the next terms in the sequence" question (consider checking OEIS first). Please provide as much context as possible. 2. Mathematical ideas related to pattern recognition, ...

0answers
226 views

### Theoretical proof of convergence of sequential weight update procedure (Neural Networks and Machine Learning)

My question is at the bottom. (Most of the descriptive words come from Chris. Bishop's Neural Networks for Pattern Recognition) Let $w$ be the weight vector of the neural network and $E$ the error ...
1answer
22 views

### Pattern finding algorithms

I am working on a server that will update a list each day. The list will look like the following example. ...
2answers
32 views

### How to count the number of x in a rows in a larger set.

For example, I have 4 in a row like so: xxxx I can see that it has 2 xxx in it and 3 xx. ...
0answers
13 views

### all possible patterns [closed]

I have 13 football games and each has only 3 posaibilities thats is home-win or draw or away-win (1-X-2). I want to find all possible patterns of winning all the thirteen games eg (22XX11X2111X2). HOW ...
1answer
28 views

### Recognising patterns and turning it into a formula

On a coordinate plane lets name a move dot A. The dot A moves each day. On day 1, it moves 1 in the x- axis direction. On day 2 it moves $2^2$ in the y- axis direction. On day 3 it moves -$3^2$ in the ...
4answers
16k views

### Finding formula for the nth partial sum

A few days ago, I asked for some clarification about pattern recognition and the n-th partial sum for infinite series. Although the explanation given was top-notch (thanks again), I'm still having ...
1answer
46 views

### Analysis of coefficients of $x^k+\dfrac1{x^k}$ polynomials

Given $x+\dfrac1x=n$, I derived several expressions in terms of $n$ to solve for $x^k+\dfrac1{x^k}$ and put them in a chart as shown below. My questions is how are the coefficients of these ...
3answers
18k views

### Predict next number from a series

Which methods I can use to predict next number from a series of numbers ? I know the min & max possible number in advance.
0answers
8 views

1answer
19 views

2answers
334 views

### Find a formula for the sequence 1,3,6,10,15,…

Write a formula/formulae for the following sequence: b). 1,3,6,10,15,... I am not getting any pattern here, from which to derive a formula. This sequence does not look like the examples I ...
2answers
58 views

### Finding the general term of a sequence (if there's any)

I would like to know if it's possible to find an expression for the following sequence $\;\{a_n\},\;n=0,\,1,\,2,\,3,\,\dots\;$ $1, 3 , 7, 13, 21...$ Someone would like to explain me what I have to ...
1answer
71 views

### State machine scenario: finding invariant

Alice, Bob, and Charles want to evenly distribute a dozen doughnuts. Initially, Alice has 5, Bob has 3, and Charles has 4. However, they want to do it according to the following rules: 1) Bob may ...
2answers
61 views

### Find mising numbers from a sequence 1,4,?,16,?,36,? [closed]

Please help me find the number absent in the line for the follow sequence $1,4,?,16,?,36,?$. For example I know the absent number in the sequence $5,0,-5,\_,\_,$, they are $-15,-20$. But I didn't ...
3answers
3k views

### What is the next picture in this sequence?

I was reading a book on logical reasoning and came across the following: Can anyone give me the answer to the question. We want the next sequence ?
1answer
29 views

### how to find formula that matches pattern

I have a pattern that I'm struggling to find the formula for. For inputs of 0 - 3, the expected result is 0. For inputs 4 - 6, the expected result is 3. 7 - 9 should output 6. 10 - 12 should output ...
3answers
39 views

### Sum of Odd Numbers make Squares

Look at this: 1 (+3) 4 (+5) 9 (+7) 16 (+9) 25 (+11) 36 (+13) 49 And so forth, you get the idea. Why do they make up this pattern? And is there any special name for this ...
3answers
348 views

### figuring out an integer function

$f(1) = 1\\ f(2) = 2\\ f(3) = 6\\ f(4) = 20\\ f(5) = 70\\ f(6) = 252\\ f(7) = 924\\ f(8) = 3432\\ f(9) = 12870$ Then what is $f(n)$ (where $n > 0$)? I though about many many possibilities but ...
2answers
273 views

### Finding the general formula of a sequence: $3,8,23,68,203,608,\cdots$

I have the following sequence : $$3,8,23,68,203,608,\cdots$$ I have found that definition by recurrence of this is $$a(n)=3a(n-1)-1$$ where $a_0=3$ as the first term. I want to find the explicit ...
1answer
91 views

### Find the pattern sequence

I'm trying to help my grandchild with $6$th grade math homework. The question given is: $$3.5,\ \ 13,\ \ 41.5,\ \ 127, \cdots$$ What are the next $3$ numbers?
3answers
81 views

### What's the generating formula for this sequence [closed]

Can someone help me finding the generating formula for this sequence? $$[1,1,3,5,5,7,9,9,11,13,13...]$$ Thanks!