Stella Octangula Number

Author

Eric W. Weisstein
December 28, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Definition

StellaOctangulaNumber[n]

OctahedralNumber[n]+8TetrahedralNumber[n-1]//Factor

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

Generating Function

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

Series[%,{x,0,10}]

Sum[StellaOctangulaNumber[n](x^n),{n,0,∞}]//Factor

Squares

Reduce[StellaOctangulaNumber[n]==m^2&&m>0&&n>0,{m,n},Integers]

Reduce[StellaOctangulaNumber[n]==m^2&&0<m<10^6&&0<n<10^6,{m,n},Integers]//Timing