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A098581 Expansion of (1+2*x+4*x^2)/(1-x-8*x^4). 1

%I

%S 1,3,7,7,15,39,95,151,271,583,1343,2551,4719,9383,20127,40535,78287,

%T 153351,314367,638647,1264943,2491751,5006687,10115863,20235407,

%U 40169415,80222911,161149815,323033071,644388391,1286171679,2575370199

%N Expansion of (1+2*x+4*x^2)/(1-x-8*x^4).

%H Harvey P. Dale, <a href="/A098581/b098581.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,8).

%F a(n) = a(n-1) + 8*a(n-4).

%F a(n) = Sum_{k=0..n} binomial(n-k, floor(k/3)) * 2^k.

%t CoefficientList[Series[(1+2x+4x^2)/(1-x-8x^4),{x,0,40}],x] (* or *) LinearRecurrence[{1,0,0,8},{1,3,7,7},40] (* _Harvey P. Dale_, Feb 04 2015 *)

%o (PARI) x='x+O('x^30); Vec((1+2*x+4*x^2)/(1-x-8*x^4)) \\ _G. C. Greubel_, Feb 03 2018

%o (MAGMA) I:=[1,3,7,7]; [n le 4 select I[n] else Self(n-1) + 8*Self(n-4): n in [1..30]]; // _G. C. Greubel_, Feb 03 2018

%Y Cf. A078467, A097334.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Sep 16 2004

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Last modified April 7 01:11 EDT 2020. Contains 333291 sequences. (Running on oeis4.)