A144899 Expansion of x/((1-x-x^3)*(1-x)^5).

0, 1, 6, 21, 57, 133, 280, 547, 1010, 1785, 3047, 5058, 8208, 13075, 20513, 31781, 48732, 74090, 111856, 167903, 250848, 373330, 553883, 819681, 1210561, 1784919, 2628351, 3866317, 5682701, 8347012, 12254249, 17983326, 26382698, 38695852, 56745223, 83201736

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 (6,-15,21,-20,16,-11,5,-1).

Crossrefs

6th column of A144903.

Cf. A000930, A050228, A077868, A144898, A144900, A144901, A144902, A144903, A144904, A226405.

Cf. A078012, A099567, A135851.

Programs

Magma

A144899:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+4, j+5): j in [0..Floor((n+4)/3)]]) >;
[A144899(n): n in [0..40]]; // G. C. Greubel, Jul 27 2022

Maple

a:= n-> (Matrix(8, (i, j)-> if i=j-1 then 1 elif j=1 then [6, -15, 21, -20, 16, -11, 5, -1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x/((1-x-x^3)(1-x)^5), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)

SageMath

def A144899(n): return sum(binomial(n-2*j+4, j+5) for j in (0..((n+4)//3)))
[A144899(n) for n in (0..40)] # G. C. Greubel, Jul 27 2022

Formula

G.f.: x/((1-x-x^3)*(1-x)^5).

From G. C. Greubel, Jul 27 2022: (Start)

a(n) = Sum_{j=0..floor((n+4)/3)} binomial(n-2*j+4, j+5).

a(n) = A099567(n+4, 5). (End)