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Questions tagged [integer-sequence]

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14
votes
10answers
5k views

Fibonacci Sequence Generator

I'm trying to write a function in Workbench which will generate a Fibonacci sequence starting with F0 = 0 and F1 = 1. So far I ...
48
votes
8answers
2k views

Is it possible to invoke the OEIS from Mathematica?

I had always wondered if there might be a way to write a function, which I'll call OEISData[], that more or less works as a curated data function for The On-Line ...
24
votes
3answers
571 views

Speeding up the built-in Rudin-Shapiro and Thue-Morse sequence functions

Version 10.2 introduced two well-studied sequences as functions: the (Golay-)Rudin-Shapiro sequence (RudinShapiro[]) and the (Prouhet-)Thue-Morse sequence (...
8
votes
2answers
1k views

Finding the coefficient of a certain power in a generating function

I want to compute $(t^1+\dots +t^5)(t^2+\dots+ t^6)(t^3+\dots +t^9)$ and find the coefficient of $t^{15}$ for example. $t$ is an indeterminate Now in Maple this is simply as ...
10
votes
2answers
741 views

How to construct rectangular figures from the Fibonacci numbers?

How do you construct rectangular figures ("golden rectangles") using the Fibonacci numbers in Mathematica using graphics? I know that the basis of the construction of these figures are the formulae ...
10
votes
9answers
3k views

How can I make a Tribonacci sequence in the form of a list?

How can I make a Tribonacci sequence that is in listing form? it suppose to look like the Fibonacci sequence but I couldn't get ...
11
votes
2answers
313 views

Animating a growing ListPlot

I stumbled upon this (rather contrived but interesting) integer sequence. As it exhibits quite different behaviour at different scales, I would like to generate an animated ...
9
votes
5answers
15k views

How to detect if a sequence of integers is consecutive

I'm not a math-guy really (a programmer actually) and this is my first question. And excuse me if I can not explain my problem good. The problem is I have a sequence of integers and I want to detect ...
1
vote
1answer
182 views

Finding recurrence formulas from procedural code and output lists associated with integer sequences

This code outputs 37 sequences and takes about 15-minutes to run. I would like to be able to see how many and which variables { i, j, k, m, n } each of the 37 ...
10
votes
1answer
160 views

How do I expand StirlingS2[n, 10] in terms of elementary functions?

I know that it is possible to expand StirlingS2[n, 10] in terms of elementary functions of n. I tried ...
11
votes
4answers
3k views

How to implement recursive function

I'm trying to do the following (taken from an answer by Watson to my question on Math SE): Start with $x_1=2$, say. Then define $$x_{n+1} = |\{i \in \{1,\dots,n-1\} \;:\; x_i=x_n\}|$$ i.e. number ...
6
votes
1answer
110 views

Are there different Method options that can be used with FindSequenceFunction?

The help page states that Method is an option to use with FindSequenceFunction, but I don't find any further information. (There ...
3
votes
2answers
177 views

solve for two variables for each n related to Collatz conjecture

For this code, for each x I would like to solve for all value ranges for c1 and c2 in a bounded range ie c1 and c2 in the range of real numbers +-100 for c1 and c2 for each x, which combined give "...
3
votes
4answers
469 views

Print all numbers from a sequence which don't contain the digit 7

so i have this: Cases[RecurrenceTable[{a[n + 1] == 7 a[n] + n, a[1] == 1}, a, {n, 7}], Except[7]] But i noticed that it will only exclude numbers that are 7, and ...
2
votes
2answers
97 views

Mathematica analog to Wolfram|Alpha dataset analysis [closed]

I have a set of sequences with length 8,48,480,5760,.. and would like to do sequence analysis on them. I plugged the length 8 sequence into wolframalpha: https://www.wolframalpha.com/input/?i=11,+2,+...
3
votes
2answers
99 views

How do I determine the 15th Lucas term in the 3rd order?

I want to implement the Lucas n-Step Number. This command taken from here doesn't seem to work, am I using the right command? ...
3
votes
1answer
537 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it doesn'...