Centered Pentagonal Number

DOWNLOAD Mathematica Notebook CenteredPentagonalNumber

A centered polygonal number consisting of a central dot with five dots around it, and then additional dots in the gaps between adjacent dots. The general term is (5n^2+5n+2)/2, and the first few such numbers are 1, 6, 16, 31, 51, 76, ... (OEIS A005891). The generating function of the centered pentagonal numbers is

 (x^2+3x+1)/((1-x)^3)=1+6x+16x^2+31x^3+....

Wolfram Web Resources

Mathematica »

The #1 tool for creating Demonstrations and anything technical.

Wolfram|Alpha »

Explore anything with the first computational knowledge engine.

Wolfram Demonstrations Project »

Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.

Computerbasedmath.org »

Join the initiative for modernizing math education.

Online Integral Calculator »

Solve integrals with Wolfram|Alpha.

Step-by-step Solutions »

Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own.

Wolfram Problem Generator »

Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.

Wolfram Education Portal »

Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more.

Wolfram Language »

Knowledge-based programming for everyone.