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Figurate Numbers

Generate triangular, square, pentagonal, hexagonal, and tetrahedral numbers, look up a term, or test membership.

A figurate number counts the dots needed to build a regular geometric shape. This tool covers five common families. Indexing is 1-based, so term 1 is the smallest member.

Triangular = n(n+1)/2, square = n², pentagonal = n(3n−1)/2, hexagonal = n(2n−1), tetrahedral = n(n+1)(n+2)/6.

Generate first K terms

Up to 1000 terms.

Look up the nth term

Test a number