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A144902 revision #11

A144902

Expansion of x/((1-x-x^3)*(1-x)^8).

0, 1, 9, 45, 166, 505, 1342, 3224, 7161, 14938, 29602, 56211, 102973, 182963, 316694, 535947, 889454, 1451305, 2333356, 3703510, 5812615, 9034001, 13921551, 21294946, 32364747, 48915873, 73576675, 110213470, 164508959, 244810154, 363371304, 538175735

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,85,-134,154,-140,106,-65,29,-8,1).

FORMULA

G.f.: x/((1-x-x^3)*(1-x)^8).

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

a(n) = Sum_{j=0..floor((n+7)/3)} binomial(n-2*j+7, j+8).

a(n) = A099567(n+7, 8). (End)

MAPLE

a:= n-> (Matrix(11, (i, j)-> if i=j-1 then 1 elif j=1 then [9, -36, 85, -134, 154, -140, 106, -65, 29, -8, 1][i] else 0 fi)^n)[1, 2]: seq(a(n), n=0..40);

MATHEMATICA

CoefficientList[Series[x/((1-x-x^3)(1-x)^8), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)

PROG

(Magma)

A144903:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+7, j+8): j in [0..Floor((n+7)/3)]]) >;

[A144903(n): n in [0..40]]; // G. C. Greubel, Jul 27 2022

(SageMath)

def A144903(n): return sum(binomial(n-2*j+7, j+8) for j in (0..((n+7)//3)))

[A144903(n) for n in (0..40)] # G. C. Greubel, Jul 27 2022

CROSSREFS

9th column of A144903.

Cf. A099567.