Explanation of Terms Used in Reply From
The following (imaginary) example shows all
the different types of lines that may appear in a reply
from the OnLine Encyclopedia of Integer Sequences.
[For a description of the Internal Format
used in the database, click
here.]
Click on the heading to get more information.
ID Number: A004001 (Formerly M0276 and N0101))
Sequence: 1,1,1,0,0,1,1,2,0,0,1,1,2,2,2,4,1,2,0,0,3,4,6,6,8,8,10,10,9,9,7,5,2,0,
7,10,18,22,29,32,41,43,49,50,54,53,54,50,46,38,30,18,6,8,25,43,62,82,
108,129,155
Signed: 1,1,1,0,0,1,1,2,0,0,1,1,2,2,2,4,1,2,0,0,3,4,6,6,8,8,10,10,9,9,7,
5,2,0,7,10,18,22,29,32,41,43,49,50,54,53,54,50,46,38,30,
18,6,8,25,43,62,82,108,129,155
Name: Bell or exponential numbers: ways of placing n labeled balls into n
indistinguishable boxes.
Comments: On first day, each gossip has his own tidbit. On each successive day, disjoint pairs of
gossips may share tidbits (over the phone). After a(n) days, all gossips have all
tidbits.
References R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. AddisonWesley,
Reading, MA, 1990, p. 329.
C. L. Mallows, Conway's challenge sequence, Amer. Math. Monthly, 98 (1991), 520.
Links: D. E. Iannucci and D. MillsTaylor, On Generalizing the Connell Sequence,
J. Integer Sequences, Vol. 2, 1999, #7.
Formula: a(n)=(1/4)*n^2*(n^2+3).
Example: a(24)=4 because we can form 2, 4, 24 and 42.
Maple: a:=proc(n) option remember; if n<=2 then 1 else a(a(n1))+a(na(n1)); fi; end;
Math'ca: dtn[L_]:=Fold[2#1+#2&,0,L]; f[n_]:=dtn[Reverse[1IntegerDigits[n,2]]];
Table[f[n],{n,0,100}]
Program: (PARI.2.0.11) direuler(p=2,101,1/(1(kronecker(5,p)*(XX^2))X))
See also: Cf. A039800
Keywords: sign,nice,easy
Offset: 5
Author(s): Christian G. Bower (bowerc(AT)usa.net), February 8, 1999.
Extension: Extended by David Wilson (wilson(AT)ctron.com), Mar 10, 1999.
Explanation of the Different Lines

The Anumber (for example A000108) is the absolute catalogue number of the sequence.
It consists of A followed by 6 digits.

Some sequences also have a 4digit Mnumber,
such as M1459, which is the number they carried in
"The Encyclopedia of Integer Sequences"
by N.J.A. Sloane and S. Plouffe, Academic Press, San Diego, CA, 1995.

Some older sequences also have a 4digit Nnumber,
such as N0577, which is the number they carried in
the "Handbook of Integer Sequences",
by N. J. A. Sloane, Academic Press, NY, 1973.
 These lines give the beginning of the sequence.

For example:
0,1,1,2,3,5,8,13,21,34,55,89,144,...
 Ideally the entry gives enough terms to fill
about three lines on the screen.
 If the sequence contains negative numbers then the Sequence
lines give the absolute values of the terms.
 The terms must be integers.
 If the terms are fractions,
then the numerators and denominators appear as separate sequences,
labeled with the Keyword "frac", and with links
connecting the two sequences.
 Only sequences that are welldefined and of general interest are included.
 These lines give the beginning of the sequence,
in the case that some of the terms are negative.
 The Ramanujan numbers, sequence
A000594,
are a famous example.
 In such cases the
Sequence
lines give the beginning of the sequence as unsigned numbers.
These numbers match onetoone with the numbers in the "Signed" lines.
 The "Name" line gives a brief description or definition of the sequence.

For example: The even numbers.
 In the description, a(n) usually denotes the nth term
of the sequence, and n is a typical subscript.

For example: a(n) = a(n1) + a(n3).
 In some cases however n denotes a typical
term in the sequence.

For example: n and n+1 have
the same number of divisors.
 Additional remarks about the sequence that
do not fit into any of the other lines
(additional situations where the sequence occurs,
for instance).
 References where information about the sequence can be found.
 Whenever possible the reference gives full bibliographical
information:

For an article in a journal: author(s), title of article, name of journal, volume,
issue number if relevant, year, starting and ending page
numbers, etc.

For a book: author(s), title, publisher,
place, year, edition, page numbers where sequence appears, etc.

For an article in a book:
author(s), title of article, page numbers, editors' names,
title of book, publisher, place, year, etc.
 Links related to this sequence
 Preferred format:
J. B. Smith, < a href = " http : // www.this.that.com/etc/etc.html ">Title< /a >
 spaces have been inserted to make it visible, but you should
not insert any spaces of course.
In other words, the format is
Author, <a href="http://www.etc.etc/file">Title</a>
 Web page addresses can change very quickly, so if you find
a link that is broken,
please add a comment to that link — you might say, for example, [broken link?  ~~~~] (the four tildes will be transformed into your signature).
 These lines give expanded information or examples to illustrate the
initial terms of the sequence.
 For instance:
4=2^2, so a(4)=1; 5=1^2+2^2=2^2+1^2, so a(5)=2.
 If the sequence is formed from the coefficients of a power series,
this line can be used to show the beginning of the series.
 For instance:
1+3600*q^3+101250*q^4+...
 If the sequence is formed from the decimal expansion
or continued fraction expansion of a real number,
this line may show the actual decimal expansion.
 For instance:
3.141592653589793238462643383279502884...
 If the sequence is formed by reading the rows
of an
array,
this line may show the beginning of the array
(see the
Keywords "tabl" and "tabf" below.)
 For instance:
{1}; {1,1}; {1,2,1}; {1,3,3,1}; {1,4,6,4,1}; ...
 These lines give Maple code to produce the sequence. Examples:

f:=i>if isprime(i) then 1 else 0; fi; [seq(f(i),i=0..100)];

for i from 1 to 100 do if isprime(i) then print(nops(factorset(i1))); fi; od;
 These lines give Mathematica code to produce the sequence. For example:

Table[ If[ n==1,1,LCM@@Map[ (#1[ [ 1 ] ]1)*#1[ [ 1 ] ]^(#1[ [ 2 ] ]1)&, FactorInteger[ n ] ] ],{n,1,70} ]
 These lines give a program in some other language that will produce the sequence. Examples:

(PARI) v=[];for(n=0,60,if(isprime(n^2+n+41),v=concat(v,n),));v

(MAGMA) R := ReedMullerCode(2,7); print(WeightEnumerator(R));

(Sage) CuspForms( Gamma1(1), 12, prec=100).0;
 These lines gives crossreferences to related sequences. Examples:

Cf. A006546, A007104, A007203.

a(n) = A025582(n)^2+1.

Sequence in context. This line show the three sequences
immediately before and after the sequence
in the lexicographic listing. Example:

Sequence in context: A036656 A000055 A006787 this_sequence A036648 A047750 A072187

Adjacent sequences. This line show the three sequences
whose Anumbers are
immediately before and after the Anumber of the sequence.
Example:

Adjacent sequences: A000989 A000990 A000991 this_sequence A000993 A000994 A000995
These lines give keywords describing the sequence.
At present the following keywords are in use.
 base: Sequence is dependent on base used
 bref: Sequence is too short to do any analysis with
 cofr: A continued fraction expansion of a number
 cons: A decimal expansion of a number
 core: An important sequence
 dead: An erroneous or duplicated sequence (the table
contains a number of incorrect sequences that have appeared in the literature,
with pointers to the correct versions)
 dumb: An unimportant sequence
 dupe: Duplicate of another sequence
 easy: It is easy to produce terms of this sequence
 eigen: An eigensequence: a fixed
sequence for some transformation  see the files
transforms and
transforms (2) for further information.
 fini: A finite sequence
 frac: Numerators or denominators of sequence of rational numbers
 full: The full sequence is given (implies that the sequence is finite)
 hard: Next term is not known and may be hard to find. Would someone please extend this sequence?
 hear: A sequence worth listening to.
 less: This is a less interesting sequence
and is less likely to be the one you were looking for.
 look: A sequence with an interesting graph.
 more: More terms are needed! Would someone please extend this sequence?
 mult: Multiplicative: a(mn)=a(m)a(n) if g.c.d.(m,n)=1
 new: New (added or modified within last two weeks, roughly)
 nice: An exceptionally nice sequence
 nonn: A sequence of nonnegative numbers (more precisely, all the displayed terms are nonnegative; it is not excluded that later terms in the sequence become negative)
 obsc: Obscure, better description needed
 probation: Included on a provisional basis,
but may be deleted later at the discretion of the editor.
 sign: Sequence contains negative numbers
 tabf: An irregular (or funnyshaped)
array of numbers made into a sequence by reading it row by row
 tabl: A regular array of numbers,
such as Pascal's triangle, made into a sequence by reading it row by row
 uned: Not edited. The editors normally check all incoming sequences to make sure that:
 the sequence is worth including
 the definition is sensible
 the sequence is not already in the database
 the English is correct
 the different parts of the entry all have the correct prefixes: crossreferences are in %Y lines, formulae in %F lines, etc.
 any %H lines are correctly formatted (this is easy to get wrong)
 etc.
The keyword "uned" indicates that this sequence needs editing. If you can help by editing the entry, please do so!
 unkn: Little is known; an unsolved problem;
anyone who can find a formula or recurrence is urged to
add it to the entry.
 walk: Counts walks (or selfavoiding paths)
 word: Depends on words for the sequence in some language
 This line usually gives the subscript of the first term in the sequence.

For example:
the
Fibonacci numbers
F(0), F(1), F(2), ... begin
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,...
and the subscript of the initial term is 0,
so the "Offset" line is
0
 If the sequence gives the decimal expansion of a constant, the offset is
the number of digits before the decimal point.

For example, the speed of light is
299792458 (m/sec),
giving the sequence
2,9,9,7,9,2,4,5,8,
with offset
9
.

In the internal format,
there is a second offset, which says which
term (counting from the left, and starting with 1), first
exceeds 1 in absolute value. This is set to 1 if all the
terms are 0 or +1.
 This line gives the name
of the person or persons who contributed the sequence. For example:
Clark Kimberling. This name will usually be an active link to the user page of the submitter on the OEIS wiki.
 E stands for
Extensions,
Errors or
Edited.
These lines contain information about sequences
that have been significantly extended,
errors that have been corrected, or entries in the database
that have been edited by someone.
 The errors might be in an earlier version of the entry in the
database or in the published literature.
 Examples:

Corrected and extended by Henry Bottomley (se16(AT)btinternet.com), Jan 01 2002

The sixth term is incorrect in the book by Smith and Jones.

Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jan 02 2002
 The database also contains a number of sequences based
on triangular or square arrays,
such as Pascal's Triangle:
          1         
         1   1        
        1   2   1       
       1   3   3   1      
      1   4   6   4   1     
     1   5   10   10   5   1    
    ...   ...   ...   ...   ...   ...   ...   
When read by rows this produces the sequence
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, ...,
Sequence
A007318.

Square arrays are usually read by antidiagonals. For example, the Nimaddition table:
0  1  2  3  4  5 
1  0  3  2  5  4 
2  3  0  1  6  7 
3  2  1  0  7  6 
4  5  6  7  0  1 
.  .  .  .  .  . 
when read by antidiagonals produces the sequence
0, 1, 1, 2, 0, 2, 3, 3, 3, 3, 4, 2, 0, 2, 4, ...,
Sequence
A003987.
 The typical term in these arrays is usually denoted by a(n,k) (sometimes T(n,k))
in the Formula lines.
 The Example lines for these sequences
usually show the beginning of the twodimensional array.
 These sequences are usually indicated by the Keyword tabl.
 Some ordinary (onedimensional) sequences also have the
keyword tabl, indicating that they can also be regarded as
arrays.
 The Keyword tabf indicates a sequence
formed by reading a "funnyshaped" array. More precisely,
this a sequence where the array cannot be recovered simply by
breaking up the sequence into chunks
of successive lengths 1, 2, 3, 4, 5, ...
Typically one has to use chunks of lengths
1, 1, 2, 2, 3, 3, 4, 4, 5, 5, ... or 1, 3, 5, 7, 9, 11, 13, ...
for "tabf" sequences.
See
A028297
and
A027113
for examples.
Wolfdieter Lang has a very nice program
that will format both "tabl" and "tabf" sequences.
It is not finished yet but there is a preliminary
version at
http://wwwitp.physik.unikarlsruhe.de/~wl/Anumbertest.html
