OFFSET
0,2
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 (15,-78,210,79,-225).
FORMULA
G.f.: (38*x^4+127*x^3-57*x^2+13*x-1) / ((1-x) * (9*x-1) * (x+1) * (25*x^2-6*x+1)).
E.g.f.: (2*exp(3*x)*cos(4*x) + 5*cosh(x) + cosh(9*x) + sinh(x) + sinh(9*x))/8. - Stefano Spezia, Nov 10 2024
EXAMPLE
a(2)=9 corresponds to the words SSSS, TTTT, UUUU, TTUU, TUUT, UUTT, TUTU, UTUT, UTTU.
MATHEMATICA
LinearRecurrence[{15, -78, 210, 79, -225}, {1, 2, 9, 62, 689}, 22] (* James C. McMahon, Nov 10 2024 *)
CoefficientList[Series[(38*x^4+127*x^3-57*x^2+13*x-1)/((1-x)*(9*x-1)*(x+1)*(25*x^2-6*x+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 11 2025 *)
PROG
(Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (38*x^4+127*x^3-57*x^2+13*x-1) / ((1-x) * (9*x-1) * (x+1) * (25*x^2-6*x+1)))); // Vincenzo Librandi, Oct 11 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sean A. Irvine, Nov 09 2024
STATUS
approved