OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1791
G. Dresden and Y. Li, Periodic Weighted Sums of Binomial Coefficients, arXiv:2210.04322 [math.NT], 2022.
László Németh and László Szalay, Sequences Involving Square Zig-Zag Shapes, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
Index entries for linear recurrences with constant coefficients, signature (8,-21,20,-5).
FORMULA
a(n) = (1/5)*Sum_{r=1..9} sin(r*Pi/10)*sin(2*r*Pi/5)*(2*cos(r*Pi/10))^(2*n+1).
a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4).
G.f.: x*(-1+x)*(-1+3*x)/(1-8*x+21*x^2-20*x^3+5*x^4).
a(n) = Sum_{k=0..n} binomial(2*n,n+k)*(k|20), where (k|20) represents the Kronecker symbol. - Greg Dresden, Oct 09 2022
MAPLE
with(NumberTheory): a := n -> add(binomial(2*n, n+k)*KroneckerSymbol(k, 20), k = 0..n): seq(a(n), n = 1..28); # Peter Luschny, Oct 14 2022
MATHEMATICA
Rest@ CoefficientList[Series[x (-1 + x)*(-1 + 3*x)/(1 - 8 x + 21 x^2 - 20 x^3 + 5 x^4), {x, 0, 24}], x] (* Michael De Vlieger, Aug 04 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Herbert Kociemba, Jun 14 2004
STATUS
approved