A144901 Expansion of x/((1-x-x^3)*(1-x)^7).

0, 1, 8, 36, 121, 339, 837, 1882, 3937, 7777, 14664, 26609, 46762, 79990, 133731, 219253, 353507, 561851, 882051, 1370154, 2109105, 3221386, 4887550, 7373395, 11069801, 16551126, 24660802, 36636795, 54295489, 80301195, 118561150, 174804431, 257430410

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 (8,-28,57,-77,77,-63,43,-22,7,-1).

Crossrefs

8th column of A144903.

Cf. A099567.

Programs

Magma

A144901:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+6, j+7): j in [0..Floor((n+6)/3)]]) >;
[A144901(n): n in [0..40]]; // G. C. Greubel, Jul 27 2022

Maple

a:= n-> (Matrix(10, (i, j)-> if i=j-1 then 1 elif j=1 then [8, -28, 57, -77, 77, -63, 43, -22, 7, -1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x/((1-x-x^3)(1-x)^7), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)

SageMath

def A144901(n): return sum(binomial(n-2*j+6, j+7) for j in (0..((n+6)//3)))
[A144901(n) for n in (0..40)] # G. C. Greubel, Jul 27 2022

Formula

G.f.: x/((1-x-x^3)*(1-x)^7).

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

a(n) = Sum_{j=0..floor((n+6)/3)} binomial(n-2*j+6, j+7).

a(n) = A099567(n+6, 7). (End)