OFFSET
0,3
COMMENTS
This sequence is fundamental for the coefficient sequences for the nonnegative powers of rho(11) = 2*cos(Pi/n) (length ration (smallest diagonal)/side in the regular 11-gon (Hendecagon)) when written in the power basis of the degree 5 number field Q(rho(11)). See A187360 for the minimal polynomial of rho(11) which is C(11, x) = x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1. See A231182-5 for these coefficient sequences.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..3532
Genki Shibukawa, New identities for some symmetric polynomials and their applications, arXiv:1907.00334 [math.CA], 2019.
Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-3,1).
FORMULA
G.f.: 1/(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)=1, a(-4)=a(-3)=a(-2)=a(-1)=0.
MATHEMATICA
CoefficientList[Series[1/(1-x-4x^2+3x^3+3x^4-x^5), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 4, -3, -3, 1}, {1, 1, 5, 6, 20}, 50] (* Harvey P. Dale, Nov 13 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Nov 05 2013
STATUS
approved