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Template:Sequence/list/names
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< Template:Sequence | list
The following documentation is located at Template:Sequence/list/names/doc. [<Edit> Template:Sequence/list/names/doc]
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[⧼Purge⧽ Template:Sequence/list/names]
The {{sequence/list/names}} (or {{seq/list/names}}) database template uses sequence names "database" tables templates (of A-numbers and their respective sequence names) and is intended to be used by the {{sequence}} OEIS Wiki user interface template (which shows a tooltip with the sequence name).
Contents
Contents of sequence names database tables
Autopopulating the sequence names database tables via a script
The sequence names "database" is to be split in sections (tables), with 1000 sequence names per table. The sequence names "database" tables would likely have to be autopopulated via a script, since there are currently (as of June 2012) more than 200000 sequences!
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Format of sequence names database tables
The sequence names "database" tables format is the following:
- each line of the database table must have the format (including one space before the vertical pipe)
| A-number = Sequence name (text only, or HTML character entities; NO HTML tags).
- the lines must be in ascending order of A-numbers
- in sequence names, the signs = < and > are OK
- the following characters cannot be used
- HTML and TeX tags cannot be used
- log<sub>10</sub> (show as log_10 instead)
- <math>log_{10}</math> (show as log_10 instead)
- e<sup>x</sup> (show as e^x instead)
- <math>e^x</math> (show as e^x instead)
- wikitext cannot be used
Usage
- {{sequence/list/names|A-number = A-number}}
or
- {{sequence/list/names|A-number}}
or
- {{seq/list/names|A-number = A-number}}
or
- {{seq/list/names|A-number}}
Examples
Examples with valid input
Code Result {{seq/list/names|A0}} The empty sequence. (Although not in the Main OEIS, since it is NOT searchable!) {{seq/list/names|A1}} Number of groups of order n. {{seq/list/names|A01}} Number of groups of order n. {{seq/list/names|A2}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. {{seq/list/names|A002}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. {{seq/list/names|A3}} Number of classes of primitive binary forms of discriminant D = -4n; or equivalently class number of quadratic order of discriminant D = -4n. {{seq/list/names|A37}} Numbers that are not squares. {{seq/list/names|A037}} Numbers that are not squares.
Code Result Comment {{seq/list/names|A000000}} The empty sequence. (Although not in the Main OEIS, since it is NOT searchable!) {{seq/list/names|A000001}} Number of groups of order n. {{seq/list/names|A000002}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. {{seq/list/names|A000003}} Number of classes of primitive binary forms of discriminant D = -4n; or equivalently class number of quadratic order of discriminant D = -4n. {{seq/list/names|A000004}} The zero sequence. {{seq/list/names|A000095}} Number of fixed points of GAMMA_0 (n) of type i. {{seq/list/names|A000096}} n*(n+3)/2. {{seq/list/names|A000097}} Number of partitions of n if there are two kinds of 1's and two kinds of 2's. {{seq/list/names|A000098}} Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3. {{seq/list/names|A000099}} Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record. (Name truncated: vertical pipe character not allowed!)
Code Result {{seq/list/names|A000100}} a(n) = number of compositions of n in which the maximum part size is 3. {{seq/list/names|A000101}} Increasing gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps). {{seq/list/names|A000102}} a(n) = number of compositions of n in which the maximum part size is 4. {{seq/list/names|A000103}} Number of n-node triangulations of sphere in which every node has degree >= 4. {{seq/list/names|A000104}} Number of n-celled polyominoes without holes. {{seq/list/names|A000195}} log(n) rounded down. {{seq/list/names|A000196}} Integer part of square root of n. Or, number of squares <= n. Or, n appears 2n+1 times. {{seq/list/names|A000197}} (n!)!. {{seq/list/names|A000198}} Largest order of automorphism group of a tournament with n nodes. {{seq/list/names|A000199}} Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).
Code Result {{seq/list/names|A000200}} Number of bicentered hydrocarbons with n atoms. {{seq/list/names|A000201}} Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2. {{seq/list/names|A000202}} a(8i+j) = 13i + a(j), where 1<=j<=8. {{seq/list/names|A000203}} sigma(n) = sum of divisors of n. Also called sigma_1(n). {{seq/list/names|A000204}} Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3. {{seq/list/names|A000295}} Eulerian numbers (Euler's triangle: column k=2 of A008292, column k=1 of A173018) {{seq/list/names|A000296}} Number of partitions of an n-set into blocks of size >1. Also number of cyclically spaced (or feasible) partitions. {{seq/list/names|A000297}} (n+1)*(n+3)*(n+8)/6. {{seq/list/names|A000298}} Number of partitions into non-integral powers. {{seq/list/names|A000299}} Number of n-node rooted trees of height 4.
Code Result {{seq/list/names|A000400}} Powers of 6. {{seq/list/names|A000401}} Numbers of form x^2 + y^2 + 2z^2. {{seq/list/names|A000402}} Number of permutations of [n] in which the longest increasing run has length 3. {{seq/list/names|A000403}} Number of simple equifacetted 3-manifolds with n faces. {{seq/list/names|A000404}} Numbers that are the sum of 2 nonzero squares. {{seq/list/names|A000495}} Nearest integer to sinh(n). {{seq/list/names|A000496}} Restricted permutations. {{seq/list/names|A000497}} S2(j,2j+2) where S2(n,k) is a 2-associated Stirling number of the second kind. {{seq/list/names|A000498}} Eulerian numbers (Euler's triangle: column k=4 of A008292, column k=3 of A173018) {{seq/list/names|A000499}} Related to the divisor function.
Code Result {{seq/list/names|A000900}} Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details). {{seq/list/names|A000901}} Number of solutions to the rook problem on a 2n X 2n board having a certain symmetry group (see Robinson for details). {{seq/list/names|A000902}} E.g.f.: (1/2)*(exp(2x + x^2) + 1). {{seq/list/names|A000903}} Number of inequivalent ways of placing n nonattacking rooks on n X n board. {{seq/list/names|A000904}} a(n) = (n + 1) a(n - 1) + (n + 2) a(n - 2) + a(n - 3); a(1)=0, a(2)=3, a(3)=13. {{seq/list/names|A000995}} Shifts left two terms under the binomial transform. {{seq/list/names|A000996}} Shifts 3 places left under binomial transform. {{seq/list/names|A000997}} From a differential equation. {{seq/list/names|A000998}} From a differential equation. {{seq/list/names|A000999}} 5^a(n) divides C(2n,n).
Code Result {{seq/list/names|A100000}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100001}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100002}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100003}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100004}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100095}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100096}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100097}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100098}} Template:Sequence/list/names/A100000..A100999 {{seq/list/names|A100099}} Template:Sequence/list/names/A100000..A100999
Examples with invalid input
Code Result {{seq/list/names}} Sequence/list error: Argument must be an A-number! {{seq/list/names|}} Sequence/list error: Argument must be an A-number! {{seq/list/names|45}} Sequence/list error: Argument must be an A-number! {{seq/list/names|a-100}} Sequence/list error: Argument must be an A-number! {{seq/list/names|a100000}} Sequence/list error: Argument must be an A-number! {{seq/list/names|B100000}} Sequence/list error: Argument must be an A-number! {{seq/list/names|A1000000}} Sequence/list error: Argument must be an A-number between A000000 and A999999! {{seq/list/names|A}} Sequence/list error: Argument must be an A-number! {{seq/list/names|A100012!}} Sequence/list error: Argument must be an A-number!
Code
<noinclude>{{Documentation}}</noinclude><includeonly><!-- -->{{#ifeq: {{#pos:{{{A-number|{{{1|}}}}}}|A}} | 0 | {{ifinteger| {{#if: {{#sub:{{{A-number|{{{1|}}}}}}|1}} | {{#sub:{{{A-number|{{{1|}}}}}}|1}} | NOTINT! }} | {{#ifexpr: ( ( {{#sub:{{{A-number|{{{1|}}}}}}|1}} ) >= 0 ) and ( ( {{#sub:{{{A-number|{{{1|}}}}}}|1}} ) <= 999999 ) | {{#switch: {{#expr: floor ( ( {{#sub:{{{A-number|{{{1|}}}}}}|1}} ) / 1000 ) }} | 0 = {{sequence/list/names/A000000..A000999| {{{A-number|{{{1|}}}}}} }} | 1 = {{sequence/list/names/A001000..A001999| {{{A-number|{{{1|}}}}}} }} | 2 = {{sequence/list/names/A002000..A002999| {{{A-number|{{{1|}}}}}} }} | 3 = {{sequence/list/names/A003000..A003999| {{{A-number|{{{1|}}}}}} }} | 4 = {{sequence/list/names/A004000..A004999| {{{A-number|{{{1|}}}}}} }} | 5 = {{sequence/list/names/A005000..A005999| {{{A-number|{{{1|}}}}}} }} | 6 = {{sequence/list/names/A006000..A006999| {{{A-number|{{{1|}}}}}} }} | 7 = {{sequence/list/names/A007000..A007999| {{{A-number|{{{1|}}}}}} }} | 8 = {{sequence/list/names/A008000..A008999| {{{A-number|{{{1|}}}}}} }} | 9 = {{sequence/list/names/A009000..A009999| {{{A-number|{{{1|}}}}}} }} (...) | 190 = {{sequence/list/names/A190000..A190999| {{{A-number|{{{1|}}}}}} }} | 191 = {{sequence/list/names/A191000..A191999| {{{A-number|{{{1|}}}}}} }} | 192 = {{sequence/list/names/A192000..A192999| {{{A-number|{{{1|}}}}}} }} | 193 = {{sequence/list/names/A193000..A193999| {{{A-number|{{{1|}}}}}} }} | 194 = {{sequence/list/names/A194000..A194999| {{{A-number|{{{1|}}}}}} }} | 195 = {{sequence/list/names/A195000..A195999| {{{A-number|{{{1|}}}}}} }} | 196 = {{sequence/list/names/A196000..A196999| {{{A-number|{{{1|}}}}}} }} | 197 = {{sequence/list/names/A197000..A197999| {{{A-number|{{{1|}}}}}} }} | 198 = {{sequence/list/names/A198000..A198999| {{{A-number|{{{1|}}}}}} }} | 199 = {{sequence/list/names/A199000..A199999| {{{A-number|{{{1|}}}}}} }} | {{{A-number|{{{1|}}}}}} <!-- NOT in sequence names database table (return the A-number) --> }} | {{error| Sequence/list error: Argument must be an [[A-number]] between A000000 and A999999! }} }} | {{error| Sequence/list error: Argument must be an [[A-number]]! }} }} | {{error| Sequence/list error: Argument must be an [[A-number]]! }} }}<!-- --></includeonly><noinclude> [[Category:Integer sequences|*]] [[Category:Mathematics-related lists|Sequences]] [[Category:Mathematical tables|Sequences]] [[Category:Database table templates|Sequences]] </noinclude>