OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Esther M. Banaian, Generalized Eulerian Numbers and Multiplex Juggling Sequences, (2016). All College Thesis Program. Paper 24. See p. 29.
Index entries for linear recurrences with constant coefficients, signature (9,-30,47,-35,10).
FORMULA
G.f.: x^3*(2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)).
a(n) = 2 - 2^n + (2^(-1-n)*(-(5-sqrt(5))^n*(3+sqrt(5)) - (-3+sqrt(5))*(5+sqrt(5))^n)) / sqrt(5) + n. - Colin Barker, Mar 29 2017
MATHEMATICA
CoefficientList[Series[x^3 (2 - 3 x)/((1 - x)^2 (1 - 2 x) (1 - 5 x + 5 x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Mar 29 2017 *)
LinearRecurrence[{9, -30, 47, -35, 10}, {0, 0, 0, 2, 15}, 30] (* Harvey P. Dale, Aug 29 2022 *)
PROG
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0, 0, 0] cat Coefficients(R!((2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)))); // Vincenzo Librandi, Mar 29 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 28 2017
STATUS
approved