OFFSET
0,3
COMMENTS
Original name was: A sum of decreasing powers.
LINKS
Zhuorui He, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (20,-155,580,-1044,720).
FORMULA
a(n) = 6^n - 5^n - 4^n - 3^n + 3*2^n.
G.f.:(-1-636*x^4+516*x^3-153*x^2+20*x)/((6*x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
a(0)=1, a(1)=0, a(2)=-2, a(3)=24, a(4)=382, a(n) = 20*a(n-1) - 155*a(n-2) + 580*a(n-3) - 1044*a(n-4) + 720*a(n-5). - Harvey P. Dale, Sep 15 2014
E.g.f.: exp(2*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3). - Elmo R. Oliveira, Sep 12 2024
MATHEMATICA
Table[6^n-5^n-4^n-3^n+3*2^n, {n, 0, 30}] (* or *) LinearRecurrence[{20, -155, 580, -1044, 720}, {1, 0, -2, 24, 382}, 30] (* Harvey P. Dale, Sep 15 2014 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 30 2003
EXTENSIONS
a(23) from Elmo R. Oliveira, Sep 12 2024
New name from formula from Zhuorui He, Sep 05 2025
STATUS
approved