A165892 Triangular numbers of form n(n+2)(n+4).

0, 15, 105, 2145, 32640, 73920, 1906128, 2299440, 7692030528

Offset: 1

Author

Zak Seidov, Sep 29 2009

Keywords

• nonn
• fini
• full

Comments

Values of (m^2-1)/8 corresponding to ordinates of integral points on the elliptic curve: m^2 = 8*n^3 + 48*n^2 + 64*n + 1.

Corresponding values of n are given in A165893.

Crossrefs

Cf. A001219 Triangular numbers of form a(a+1)(a+2).

Programs

Mathematica

TNQ[m_]:=IntegerQ[Sqrt[1+8*m]];Do[If[TNQ[m=n*(n+2)*(n+4)],Print[m]],{n,2*10^3}]
Select[Table[n(n+2)(n+4),{n,0,2000}],OddQ[Sqrt[8#+1]]&] (* Harvey P. Dale, Feb 07 2015 *)

Extensions

"fini", "full" keywords from Max Alekseyev, Oct 01 2009

Initial 0 added by Zak Seidov, Oct 04 2009 at the suggestion of Alexander R. Povolotsky.