Truncated Tetrahedral Number

A figurate number constructed by taking the th tetrahedral number and removing the th tetrahedral number from each of the four corners,

			(1)
			(2)

The first few are 1, 16, 68, 180, 375, ... (Sloane's A005906). The generating function for the truncated tetrahedral numbers is

(3)

Ref: mathworld.wolfram.com

Gnomonic Number

A figurate number of the form  giving the area of the square gnomon obtained by removing a square of side  from a square of side ,

			(1)
			(2)

The gnomonic numbers are therefore equivalent to the odd numbers, and the first few are 1, 3, 5, 7, 9, 11, ... (Sloane's A005408). The generating function for the gnomonic numbers is

Ref: mathworld.wolfram.com

(3)

Decagonal Number

A figurate number of the form . The first few are 1, 10, 27, 52, 85, ... (Sloane's A001107). The generating function giving the decagonal numbers is

The first few odd decagonal numbers are 1, 27, 85, 175, 297, ... (Sloane's A028993), and the first few even decagonal numbers are 10, 52, 126, 232, 370, 540, ... (Sloane's A028994).

Ref: mathworld.wolfram.com