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  2. Triangular number - Wikipedia

    en.wikipedia.org/wiki/Triangular_number

    A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number , other examples being square numbers and cube numbers . The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural ...

  3. Centered triangular number - Wikipedia

    en.wikipedia.org/wiki/Centered_triangular_number

    Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...

  4. Squared triangular number - Wikipedia

    en.wikipedia.org/wiki/Squared_triangular_number

    A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.

  5. Square triangular number - Wikipedia

    en.wikipedia.org/wiki/Square_triangular_number

    Consequently, a square number is also triangular if and only if + is square, that is, there are numbers and such that =. This is an instance of the Pell equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1} with n = 8 {\displaystyle n=8} .

  6. File:Centered triangular numbers hex grid.svg - Wikipedia

    en.wikipedia.org/wiki/File:Centered_triangular...

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  7. Category:Triangles of numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Triangles_of_numbers

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  8. Tetrahedral number - Wikipedia

    en.wikipedia.org/wiki/Tetrahedral_number

    Te 12 = 364 is the total number of gifts "my true love sent to me" during the course of all 12 verses of the carol, "The Twelve Days of Christmas". [3] The cumulative total number of gifts after each verse is also Te n for verse n. The number of possible KeyForge three-house combinations is also a tetrahedral number, Te n−2 where n is the ...

  9. Doubly triangular number - Wikipedia

    en.wikipedia.org/wiki/Doubly_triangular_number

    In mathematics, the doubly triangular numbers are the numbers that appear within the sequence of triangular numbers, in positions that are also triangular numbers. That is, if T n = n ( n + 1 ) / 2 {\displaystyle T_{n}=n(n+1)/2} denotes the n {\displaystyle n} th triangular number, then the doubly triangular numbers are the numbers of the form ...

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