liminfoOEIS Reference
Free reference guide: OEIS Reference
About OEIS Reference
The OEIS Sequence Reference is a comprehensive, searchable guide to the On-Line Encyclopedia of Integer Sequences. It covers famous sequences like Fibonacci (A000045), primes (A000040), Catalan numbers (A000108), factorials (A000142), and triangular numbers (A000217), along with their closed-form expressions, recurrence relations, and generating functions.
Beyond sequence lookup, this reference explains OEIS search techniques including value-based search, keyword search, and direct A-number access. It documents sequence notation conventions such as offset, Dirichlet series, and asymptotic formulas, as well as OEIS keywords (nonn, nice, core, cons) and contribution workflows for submitting new sequences, editing entries, adding program code, and working with b-files.
Designed for mathematicians, computer scientists, and students working in combinatorics, number theory, and algorithm analysis. All processing happens locally in your browser with full dark mode support across desktop, tablet, and mobile devices.
Key Features
- Searchable database of famous OEIS sequences with A-numbers, formulas, and first terms
- Covers Fibonacci, primes, Catalan, Bell, partition numbers, and primorials with closed-form and recurrence expressions
- OEIS search techniques: value-based lookup, keyword search, author search, and direct A-number access
- Sequence notation reference including generating functions, Dirichlet series, and asymptotic formulas
- OEIS keyword guide covering nonn, easy, hard, nice, core, cons, and frac classifications
- Contribution workflow documentation for submitting sequences, editing entries, and adding program code
- b-file format reference with download URLs and submission guidelines
- Cross-reference entries linking related sequences such as Lucas numbers, golden ratio, and Tribonacci
Frequently Asked Questions
How do I search for a sequence on OEIS?
You can search OEIS by entering comma-separated sequence values (e.g., 1,1,2,3,5,8,13 returns A000045 for Fibonacci), by keyword (e.g., "fibonacci" or "catalan"), by author name (author:Sloane), or by directly navigating to an A-number URL like https://oeis.org/A000045. This reference documents all these search methods with examples.
What is the difference between a closed-form formula and a recurrence relation?
A closed-form formula gives the n-th term directly without referencing previous terms, such as a(n) = n(n+1)/2 for triangular numbers. A recurrence relation defines each term using previous terms, such as a(n) = a(n-1) + a(n-2) for Fibonacci. This reference covers both types along with generating functions and asymptotic approximations.
What do OEIS keywords like nonn, nice, and core mean?
The keyword "nonn" indicates a sequence of non-negative integers (most OEIS sequences). "nice" marks sequences of special mathematical interest (about 6,000 sequences). "core" identifies the roughly 200 most fundamental sequences including primes and Fibonacci. Other keywords include "easy/hard" for computational difficulty and "cons/frac" for constant decimal expansions and fraction sequences.
How can I contribute a new sequence to OEIS?
Create an account at oeis.org, then navigate to Contribute > New Sequence. Enter the sequence name, initial terms, formula, and references. Your submission will be reviewed by OEIS editors before publication. You can also edit existing sequences to add formulas, program code (Mathematica, Python, PARI/GP, Sage), or cross-references.
What is a b-file in OEIS and how do I use it?
A b-file is a plain text file containing extended sequence data as index-value pairs separated by spaces (e.g., "0 0\n1 1\n2 1\n3 2" for Fibonacci). You can download b-files from URLs like https://oeis.org/A000045/b000045.txt to get thousands of terms. You can also submit b-files with up to 10,000 terms for sequences that lack extended data.
What are generating functions and why are they important?
A generating function encodes an entire sequence as a power series. For example, the Fibonacci generating function is G(x) = x/(1-x-x^2). They are powerful tools in combinatorics for proving identities, finding closed forms, and analyzing asymptotic behavior. This reference covers ordinary generating functions and Dirichlet series representations.
Which famous sequences are covered in this reference?
This reference includes natural numbers (A000027), primes (A000040), Fibonacci (A000045), powers of 2 (A000079), factorials (A000142), Catalan numbers (A000108), triangular numbers (A000217), perfect squares (A000290), Bell numbers (A000110), partition numbers (A000041), primorials (A002110), squarefree numbers (A005117), and central binomial coefficients (A001405).
Is this OEIS reference free to use?
Yes, this OEIS reference is completely free with no usage limits, no account required, and no software installation needed. All data is processed locally in your browser. It is part of liminfo.com's collection of free online mathematical and scientific reference tools.