OFFSET
0,5
COMMENTS
Gives the even terms, all the odd terms are 0.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-68,112,112,64).
FORMULA
G.f.: (8*x^7+28*x^6+42*x^5-34*x^4+35*x^3-21*x^2+7*x-1) / ((4*x-1) * (4*x^2+1) * (4*x^4+8*x^3+8*x^2-4*x+1)).
a(n) = Sum_{k=0..floor(n/4)} binomial(2*n,8*k). - Seiichi Manyama, Sep 10 2025
EXAMPLE
a(4)=2 corresponds to the words SSSSSSSS and TTTTTTTT.
MATHEMATICA
CoefficientList[Series[(8*x^7+28*x^6+42*x^5-34*x^4+35*x^3-21*x^2+7*x-1)/((4*x-1)*(4*x^2+1)*(4*x^4+8*x^3+8*x^2-4*x+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 10 2025 *)
PROG
(Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((8*x^7+28*x^6+42*x^5-34*x^4+35*x^3-21*x^2+7*x-1) / ((4*x-1) * (4*x^2+1) * (4*x^4+8*x^3+8*x^2-4*x+1)))); // Vincenzo Librandi, Oct 10 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sean A. Irvine, Nov 09 2024
STATUS
approved