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 denotes the th triangular number, then the doubly triangular numbers are the numbers of the form .
The doubly triangular numbers form the sequence[1]
The th doubly triangular number is given by the quartic formula[2]
The sums of row sums of Floyd's triangle give the doubly triangular numbers. Another way of expressing this fact is that the sum of all of the numbers in the first rows of Floyd's triangle is the th doubly triangular number.[1][2]
Doubly triangular numbers arise naturally as numbers of unordered pairs of unordered pairs of objects, including pairs where both objects are the same:
When pairs with both objects the same are excluded, a different sequence arises, the tritriangular numbers which are given by the formula .[5]
Some numerologists and biblical studies scholars consider it significant that 666, the number of the beast, is a doubly triangular number.[6][7]