Truncated Tetrahedral Number

Author

Eric W. Weisstein
January 6, 2009

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

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

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

Definition

TetrahedralNumber[3n-2]-4TetrahedralNumber[n-1]//Factor

TruncatedTetrahedralNumber[n]

Table[TruncatedTetrahedralNumber[n],{n,5}]

Generating Function

GeneratingFunction[TruncatedTetrahedralNumber[n],n,x]//Factor

SeriesCoefficient[%,{x,0,n}]

Sum[(1/6) n (10-27 n+23 (n^2))(x^n),{n,0,∞}]//Factor