A144900 Expansion of x/((1-x-x^3)*(1-x)^6).

0, 1, 7, 28, 85, 218, 498, 1045, 2055, 3840, 6887, 11945, 20153, 33228, 53741, 85522, 134254, 208344, 320200, 488103, 738951, 1112281, 1666164, 2485845, 3696406, 5481325, 8109676, 11975993, 17658694, 26005706, 38259955, 56243281, 82625979, 121321831, 178067054

Offset: 0

Author

Alois P. Heinz, Sep 24 2008

Keywords

• nonn
• easy

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).

Crossrefs

7th column of A144903.

Cf. A099567.

Programs

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

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 *)

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

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)