mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words...

In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2...

number, other examples being square numbers and cube numbers. The nth triangular number is the number of dots in the triangular arrangement with n dots on...

A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns...

square root of n; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers). In the real number system...

properties of oblong, triangular, and square numbers: 1 . The number 10 for example, can be arranged as a triangle (see triangular number): But 10 cannot be...

A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other...

(thirty-six) is the natural number following 35 and preceding 37. 36 is both the square of six, and the eighth triangular number or the sum of the first eight...

As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations...

n-th square pyramidal number. The number of rectangles in a square grid is given by the squared triangular numbers. The square pyramidal number P n {\displaystyle...

7-digit prime number 1,000,405 = Smallest triangular number with 7 digits and the 1,414th triangular number 1,002,001 = 10012, palindromic square 1,006,301...

are square, then the right triangular prism is semiregular. A semiregular prism means that the number of its polygonal base's edges equals the number of...

In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center...

A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers...

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes...

reversal is a square triangular number (triangular of 57121). 1,921,525,212 : number of partitions of 264 into divisors of 264 1,934,502,740 : number of parallelogram...

initial 1. For example, each centered square number in the series is four times the previous triangular number, plus 1. This can be formalized by the...

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...

n} th triangular number, then the doubly triangular numbers are the numbers of the form T T n {\displaystyle T_{T_{n}}} . The doubly triangular numbers...

prime number 10,001,628 = smallest triangular number with 8 digits and the 4,472nd triangular number 10,004,569 = 31632, the smallest 8-digit square 10,077...

such representations of the number 17, for example, are shown below: 17 = 10 + 6 + 1 (triangular numbers) 17 = 16 + 1 (square numbers) 17 = 12 + 5 (pentagonal...

are both tetrahedral and square pyramidal. Square triangular number, the numbers that are simultaneously square and triangular Close-packing of equal spheres...

In number theory, a factoriangular number is an integer formed by adding a factorial and a triangular number with the same index. The name is a portmanteau...

A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided...

Augmented triangular prism: The result of gluing a triangular prism to a square pyramid, this has six equilateral triangle faces and two square faces. It...

is an 8 × 8 square. Its square, 2042 = 41616, is the fourth square triangular number. As a figurate number, 204 is also a nonagonal number and a truncated...

triangular number and n more than the nth square number, as given by the alternative formula n2 + n for pronic numbers. Hence the nth pronic number and...

A truncated triangular pyramid number is found by removing (truncating) some smaller tetrahedral number (or triangular pyramidal number) from each of...

of 100 and also the square of 100,000. 10,000,000,019 = smallest 11-digit prime number. 10,000,020,331 = smallest triangular number with 11 digits and...

pyramidal number and a dodecagonal number. Additionally, it is the index, in the sequence of triangular numbers, of the fifth square triangular number: 41616...