OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,36,-41,36,-27,16,-6,1).
FORMULA
G.f.: x/((1-x-x^3)*(1-x)^6).
From G. C. Greubel, Jul 27 2022: (Start)
a(n) = Sum_{j=0..floor((n+5)/3)} binomial(n-2*j+5, j+6).
a(n) = A099567(n+5, 6). (End)
MAPLE
a:= n-> (Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [7, -21, 36, -41, 36, -27, 16, -6, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);
MATHEMATICA
CoefficientList[Series[x/((1-x-x^3)(1-x)^6), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{7, -21, 36, -41, 36, -27, 16, -6, 1}, {0, 1, 7, 28, 85, 218, 498, 1045, 2055}, 40] (* Harvey P. Dale, Mar 02 2016 *)
PROG
(Magma)
A144900:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+5, j+6): j in [0..Floor((n+5)/3)]]) >;
[A144900(n): n in [0..40]]; // G. C. Greubel, Jul 27 2022
(SageMath)
def A144900(n): return sum(binomial(n-2*j+5, j+6) for j in (0..((n+5)//3)))
[A144900(n) for n in (0..40)] # G. C. Greubel, Jul 27 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 24 2008
STATUS
approved