User:BZAW31559/sandbox/figurate

n = 365

Triangular: ${\textstyle {\frac {365(365+1)}{2}}={\frac {365\times 366}{2}}={\frac {133590}{2}}=66795}$

Square: ${\textstyle 365^{2}=133225}$

Pentagonal: ${\textstyle {\frac {3(365^{2})-365}{2}}={\frac {399310}{2}}=199655}$

Hexagonal: ${\textstyle 365(2(365)-1)=266085}$

Heptagonal: ${\textstyle {\frac {5(365^{2})-3(365)}{2}}={\frac {665030}{2}}=332515}$

Octagonal: ${\textstyle 3(365^{2})-2(365)=398945}$

Nonagonal: ${\textstyle {\frac {365(7(365)-5)}{2}}={\frac {930750}{2}}=465375}$

Decagonal: ${\textstyle 4(365^{2})-3(365)=531805}$

Dodecagonal: $5(365^{2})-4(365)=664665$

Centered triangular: ${\textstyle {\frac {3(365^{2})+3(365)+2}{2}}={\frac {400772}{2}}=200386}$

Centered square: ${\textstyle 365^{2}+(365-1)^{2}=265721}$

Centered pentagonal: ${\textstyle {\frac {5(365)^{2}+5(365)+2}{2}}={\frac {667952}{2}}=333976}$

Centered hexagonal: ${\textstyle 3(365)(365-1)+1=398581}$

Centered heptagonal: ${\textstyle {\frac {7(365^{2})-7(365)+2}{2}}={\frac {930022}{2}}=465011}$

Centered octaagonal: ${\textstyle (2(365)-1)^{2}=531441}$

Centered nonagonal: ${\textstyle {\frac {(3(365)-2)(3(365)-1)}{2}}={\frac {1195742}{2}}=597871}$

Centered decagonal: ${\textstyle 5(365)^{2}+5(365)+1=667951}$

Star: ${\textstyle 6(365)(365-1)+1=797161}$

Cube: ${\textstyle 365^{3}=48627125}$