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A098582 Expansion of (1+2*x+4*x^2+8*x^3)/(1-x-16*x^5). 2

%I

%S 1,3,7,15,15,31,79,191,431,671,1167,2431,5487,12383,23119,41791,80687,

%T 168479,366607,736511,1405167,2696159,5391823,11257535,23041711,

%U 45524383,88662927,174932095,355052655,723720031,1452110159,2870716991

%N Expansion of (1+2*x+4*x^2+8*x^3)/(1-x-16*x^5).

%H G. C. Greubel, <a href="/A098582/b098582.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,16).

%F a(n) = a(n-1) + 16*a(n-5).

%F a(n) = Sum_{k=0..n} binomial(n-k, floor(k/4)) * 2^k.

%t CoefficientList[Series[(1+2*x+4*x^2+8*x^3)/(1-x-16*x^5), {x,0,50}], x] (* or *) LinearRecurrence[{1,0,0,0,16}, {1,3,7,15,15}, 50] (* _G. C. Greubel_, Feb 03 2018 *)

%o (PARI) x='x+O('x^30); Vec((1+2*x+4*x^2+8*x^3)/(1-x-16*x^5)) \\ _G. C. Greubel_, Feb 03 2018

%o (MAGMA) I:=[1,3,7,15,15]; [n le 5 select I[n] else Self(n-1) +16*Self(n-5): n in [1..30]]; // _G. C. Greubel_, Feb 03 2018

%K easy,nonn

%O 0,2

%A _Paul Barry_, Sep 16 2004

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Last modified February 22 23:14 EST 2020. Contains 332157 sequences. (Running on oeis4.)