A165892
Triangular numbers of form n(n+2)(n+4).
Original entry on oeis.org
0, 15, 105, 2145, 32640, 73920, 1906128, 2299440, 7692030528
Offset: 1
Cf.
A001219 Triangular numbers of form a(a+1)(a+2).
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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 *)
Initial 0 added by
Zak Seidov, Oct 04 2009 at the suggestion of Alexander R. Povolotsky.
A238008
Numbers n such that n*(n+3)*(n+6) is a triangular number.
Original entry on oeis.org
-5, -3, 0, 1, 10, 12, 22, 159, 639, 651, 2629
Offset: 1
1 is in the sequence because 1*4*7=28 is a triangular number.
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istriang(n)=issquare(8*n+1);
isok(n)=istriang( n*(n+3)*(n+6) );
for (n=-10^6, 10^6, if ( isok(n), print1(n,", ") ) );
\\ Joerg Arndt, Feb 17 2014
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isok(n) = ispolygonal((n-1)*n*(n+1), 3); \\ Michel Marcus, Mar 05 2014
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# for the curve y^2 + b1*x*y + b3*y = x^3 + b2*x^2 + b4*x + b5, use
# EllipticCurve([b1,b2, b3,b4,b5])
# we have y^2 + 2*y == x^3 + 18*x^2 + 72*x + 0, so need
E=EllipticCurve([0, 18, 2, 72, 0])
E.integral_points()
## Joerg Arndt, Feb 27 2014
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