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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 ...
47
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
554 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
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
292 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
14k 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 ...
10
votes
1answer
157 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
2k 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
100 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 ...
9
votes
2answers
659 views

How to construct rectangular figures from the Fibonacci numbers?

How do you construct rectangular figures using the Fibonacci numbers in Mathematica using graphics? I know that the basis of the construction of these figures are the formulae for summing the terms, ...
3
votes
4answers
467 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
84 views

Mathematica analog to Wolfram|Alpha dataset analysis

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
1answer
518 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'...
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? ...