Truncated Octahedral Number

Author

Eric W. Weisstein
January 5, 2009

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

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

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

Definition

TruncatedOctahedralNumber[n]

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

Factor[OctahedralNumber[3n-2]-6PyramidalNumber[n-1,4]]

Generating Function

Factor[6+GeneratingFunction[TruncatedOctahedralNumber[n],n,x]]

SeriesCoefficient[((x (1+34 x+55 (x^2)+6 (x^3)))/(((-1+x))^4)),{x,0,n}]

Sum[TruncatedOctahedralNumber[n](x^n),{n,∞}]//Factor

V8

Sum[(16n^3-33n^2+24n-6) x^n,{n,0,Infinity}]//Factor