Laisant's Recurrence Formula

Author

Eric W. Weisstein
April 6, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/LaisantsRecurrenceFormula.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Solution

V5.2

RSolve[a[n]==((((n-1)^2-1)a[n-1]+n a[n-2]+4(-1)^(n-1))/(n-2))&&a[2]==0&&a[3]==1,a[n],n]

V7

RSolve[a[n]==((((n-1)^2-1)a[n-1]+n a[n-2]+4(-1)^(n-1))/(n-2))&&a[2]==0&&a[3]==1,a[n],n]

Recurrence

a[1]:=0
a[2]:=0
a[3]:=1
a[n_]:=a[n]=((((n-1)^2-1)a[n-1]+n a[n-2]+4(-1)^(n-1))/(n-2))

a/@Range[10]