OFFSET
0,3
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-3,1).
FORMULA
G.f.: (1 - x)/(1-x-4*x^2+3*x^3+3*x^4-x^5).
a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 3*a(n-4) + a(n-5) for n >= 0, with a(-5)=-2, a(-4)=-1 , a(-3)=a(-2)=a(-1)=0.
a(n) = b(n) - b(n-1) for n>=0, with b(n) = A231181(n) (first differences).
EXAMPLE
rho(11)^5 = 1*1 - 3*rho(11) - 3*rho(11)^2 + 4*rho(11)^3 + 1*rho(11)^4. Approximately 26.02309649, with rho(11) approximately 1.918985947.
MATHEMATICA
LinearRecurrence[{1, 4, -3, -3, 1}, {1, 0, 4, 1, 14}, 40] (* Harvey P. Dale, Aug 03 2023 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Nov 07 2013
STATUS
approved