Is there a built in general recurrence sequence function like the binary recurrence sequence?
def a(n):
return BinaryRecurrenceSequence(a,b,c,d)
returns the sequence $U_0=c$, $U_1=d$, and $U_n=aU_{n-1}+bU_{n-2}$.
I would like something that returns $U_n=aU_{n-1}+bU_{n-2}+cU_{n-3}$
Any help is much appreciated!
If you need to compute $U_n$ efficiently - here is a way:
a=1
b=2
c=3
u0=u1=u2=1 # initial values
x = polygen(QQ)
C = companion_matrix(x^3-a*x^2-b*x-c)
def U(n):
return (vector([u0,u1,u2]) * C^n)[0]
Alternatively you can use LFSR as described at https://doc.sagemath.org/html/en/refe...
Asked: 2024-03-18 17:52:47 +0200
Seen: 97 times
Last updated: Mar 19
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.