Template:Triangle line breaks

The following documentation is located at Template:Triangle line breaks/doc. [<Edit> Template:Triangle line breaks/doc]
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You may use the {{triangle line breaks}} OEIS Wiki utility template to automatically generate the triangle line breaks in a sequence of integers for the {{number triangle}} template. Currently, up to 

t8 = 36

sequence terms are supported, giving up to 8 rows.

Usage

{{triangle line breaks|integer sequence|sep = separator}}

where

• integer sequence with up to 

  t8 = 36

  terms;
• separator is the sequence terms separator (default: ,).

The triangle line breaks are then automatically marked with two instances of separator in a row.

Examples

The code

: {{triangle line breaks| 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, }}

gives

0 ,, 0 , 1 ,, 0 , 1 , 2 ,, 0 , 1 , 2 , 3 ,, 0 , 1 , 2 , 3 , 4 ,, 0 , 1 , 2 , 3 , 4 , 5 ,, 0 , 1 , 2 , 3 , 4 , 5 , 6 ,, 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 ,,

Number triangles

The code

{{number triangle
| title =  
| rows count = 8
| rows =

{{triangle line breaks| 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, }}

| sep = ,
| f(n) = htm: ''t''{{sub|''n''}} 
}}

yields

n																				tn
0										0										0
1									0		1									1
2								0		1		2								3
3							0		1		2		3							6
4						0		1		2		3		4						10
5					0		1		2		3		4		5					15
6				0		1		2		3		4		5		6				21
7			0		1		2		3		4		5		6		7			28
			k = 0		1		2		3		4		5		6		7

The code

{{highlighted number triangle
| title = 
| type = equi
| sep = ,
| rows =

{{triangle line breaks| 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, }}

| start row = 0 | start column = 0
| rows count = 7
| row sums = yes
| f(n) = htm:
| highlight style = background: red; color: yellow; 
| highlight = d2 
}}

yields

n																		∑ n k  = 0  T  (n, k)
0									0									0
1								0		1								1
2							0		1		2							3
3						0		1		2		3						6
4					0		1		2		3		4					10
5				0		1		2		3		4		5				15
6			0		1		2		3		4		5		6			21
			k = 0		1		2		3		4		5		6

See also

• {{number triangle}} (no highlighting, but up to 16 rows)
• {{highlighted number triangle}} (to highlight either: a row, a column [of rectangular triangle], the central coefficients, a single [or all] downwards diagonal[s], a single [or all] downwards slope 1/2 diagonal[s], a single [or all] upwards diagonal[s], or a single [or all] upwards slope 1/2 diagonal[s])