Tritriangular Numbers

Author

Eric W. Weisstein
January 5, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/TritriangularNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TritriangularNumber.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

TritriangularNumber[n]

Binomial[Binomial[n+2,2],2]

Table[(1/8) n (1+n) (2+n) (3+n),{n,10}]

Generating Function

GeneratingFunction[TritriangularNumber[n],n,x]

SeriesCoefficient[-((3 x)/(((-1+x))^5)),{x,0,n}]

Sum[TritriangularNumber[n](x^n),{n,0,∞}]

Intersecting Lines Figure

pts=Table[Random[],{4},{2},{2}]

int=Intersections@@@KSubsets[Line/@pts,2];

Need to write code to only draw new lines created by connecting points of intersections

Show[Graphics[{
{Red,
LongestLine[#,.2]&/@KSubsets[Coordinates/@int,2]
},
LongestLine[#,.2]&/@Table[Join[pts[[i]],Coordinates/@int[[First/@Position[KSubsets[Range[4],2],i]]]
],{i,4}],
PointSize[.04],Red,int
},AspectRatio->Automatic,
PlotRange->All]]