The first six triangular numbers A triangular number is a number that is the sum of all of the natural numbers up to a certain number. When formed using regularly spaced dots, they tend to form a shape of either an equilateral or a right triangle , hence the name.[ 1]
For example, 10 is a "triangular number" because 10 = 1 + 2 + 3 + 4 {\displaystyle 10=1+2+3+4}
The first 25 triangular numbers are: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, and so on.
A triangular number is calculated by the equation:
n ( n + 1 ) 2 {\displaystyle {\frac {n(n+1)}{2}
References
Other polynomial numbers
Hilbert Idoneal Leyland Loeschian Lucky numbers of Euler
Fibonacci Jacobsthal Leonardo Lucas Padovan Pell Perrin
Possessing a specific set of other numbers
Congruent Knödel Riesel Sierpiński
Expressible via specific sums
Nonhypotenuse Polite Practical Primary pseudoperfect Ulam Wolstenholme
Figurate numbers
2-dimensional
centered Centered triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star non-centered Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal Dodecagonal
3-dimensional
centered Centered tetrahedral Centered cube Centered octahedral Centered dodecahedral Centered icosahedral non-centered Tetrahedral Cubic Octahedral Dodecahedral Icosahedral Stella octangula pyramidal
4-dimensional
non-centered Pentatope Squared triangular Tesseractic
Combinatorial numbers
Bell Cake Catalan Dedekind Delannoy Euler Eulerian Fuss–Catalan Lah Lazy caterer's sequence Lobb Motzkin Narayana Ordered Bell Schröder Schröder–Hipparchus Stirling first Stirling second
Wieferich Wall–Sun–Sun Wolstenholme prime Wilson
Pseudoprimes
Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Somer–Lucas pseudoprime Strong pseudoprime
Arithmetic functions and dynamics
Blum Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet Zeisel
Arithmetic functions Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related Other Dudeney Factorion Kaprekar Kaprekar's constant Keith Lychrel Narcissistic Perfect digit-to-digit invariant Perfect digital invariant
P-adic numbers -relatedDigit -composition relatedPalindromic Pandigital Repdigit Repunit Self-descriptive Smarandache–Wellin Strictly non-palindromic Undulating Digit-permutation related Cyclic Digit-reassembly Parasitic Primeval Transposable Divisor-related Equidigital Extravagant Frugal Harshad Polydivisible Smith Vampire Other
Pancake number Sorting number
