# Category:Triangular Numbers

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This category contains results about **Triangular Numbers**.

Definitions specific to this category can be found in Definitions/Triangular Numbers.

**Triangular numbers** are those denumerating a collection of objects which can be arranged in the form of an equilateral triangle.

## Subcategories

This category has the following 14 subcategories, out of 14 total.

### C

### E

### I

### R

### S

## Pages in category "Triangular Numbers"

The following 71 pages are in this category, out of 71 total.

### C

### I

- If n is Triangular then so is (2m+1)^2 n + m(m+1)/2
- If n is Triangular then so is 25n + 3
- If n is Triangular then so is 49n + 6
- If n is Triangular then so is 9n + 1
- Index of Square Triangular Number from Preceding
- Integer both Square and Triangular
- Integer is Sum of Three Triangular Numbers
- Integers not Sum of Distinct Triangular Numbers

### P

- Palindromic Indices of Palindromic Triangular Numbers
- Palindromic Triangular Numbers
- Palindromic Triangular Numbers whose Index is Palindromic
- Palindromic Triangular Numbers with Palindromic Halves
- Palindromic Triangular Numbers with Palindromic Index
- Pentagonal Number as Sum of Triangular Numbers
- Product of Consecutive Triangular Numbers
- Product of Two Triangular Numbers to make Square

### S

- Second Column and Diagonal of Pascal's Triangle consist of Triangular Numbers
- Sequence of Smallest 3 Consecutive Triangular Numbers which are Sphenic
- Sequences of 3 Consecutive Triangular Numbers which are Sphenic
- Smallest Number Expressible as Sum of at most Three Triangular Numbers in 4 ways
- Square of Odd Multiple of 3 is Difference between Triangular Numbers
- Square of Odd Number as Difference between Triangular Numbers
- Square of Triangular Number equals Sum of Sequence of Cubes
- Square of Triangular Numbers as Sum of Triangular Numbers
- Square Product of Three Consecutive Triangular Numbers
- Square Pyramidal and Triangular Numbers
- Square Sum of Three Consecutive Triangular Numbers
- Sufficient Condition for Square of Product to be Triangular
- Sum of Adjacent Sequences of Triangular Numbers
- Sum of Consecutive Triangular Numbers is Square
- Sum of Sequence of Fifth Powers
- Sum of Sequence of Reciprocals of Triangular Numbers
- Sum of Sequence of Triangular Numbers

### T

- Tetrahedral and Triangular Numbers
- There exist no 4 Consecutive Triangular Numbers which are all Sphenic Numbers
- Triangular Fermat Number
- Triangular Fibonacci Numbers
- Triangular Lucas Numbers
- Triangular Number as Alternating Sum and Difference of Squares
- Triangular Number cannot be Cube
- Triangular Number cannot be Fifth Power
- Triangular Number cannot be Fourth Power
- Triangular Number Modulo 3 and 9
- Triangular Number Pairs with Triangular Sum and Difference
- Triangular Number whose Square is Triangular
- Triangular Number/Examples
- Triangular Number/Sequence
- Triangular Numbers are Primitive Recursive
- Triangular Numbers in Geometric Sequence
- Triangular Numbers which are also Pentagonal
- Triangular Numbers which are also Square
- Triangular Numbers which are also Square/Sequence
- Triangular Numbers which are Product of 3 Consecutive Integers
- Triangular Numbers which are Sum of Two Cubes
- Triple of Triangular Numbers whose Pairwise Sums are Triangular