Editing Decagonal number (section)

== Properties ==

* Decagonal numbers consistently alternate [[Even and odd numbers#Parity in mathematics|parity]].
* <math>D_n</math> is the sum of the first <math>n</math> natural numbers congruent to 1 mod 8.
* <math>D_n</math> is number of divisors of <math>48^{n-1}</math>.
* The only decagonal numbers that are square numbers are 0 and 1.
* The decagonal numbers follow the following recurrence relations:
:<math>D_n=D_{n-1}+8n-7 , D_0=0</math>
:<math>D_n=2D_{n-1}-D_{n-2}+8, D_0=0,D_1=1</math>
:<math>D_n=3D_{n-1}-3D_{n-2}+D_{n-3}, D_0=0, D_1=1, D_2=10</math>