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Powers of 2 repeated 4 times.
5

%I #28 Jan 30 2023 11:12:15

%S 1,1,1,1,2,2,2,2,4,4,4,4,8,8,8,8,16,16,16,16,32,32,32,32,64,64,64,64,

%T 128,128,128,128,256,256,256,256,512,512,512,512,1024,1024,1024,1024,

%U 2048,2048,2048,2048,4096,4096,4096,4096

%N Powers of 2 repeated 4 times.

%C Run lengths in A173922.

%H G. C. Greubel, <a href="/A200675/b200675.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 (0,0,0,2)

%F a(n) = 2^floor(n/4).

%F G.f.: x*(1+x)*(1+x^2)/(1-2*x^4 ). - _R. J. Mathar_, Nov 21 2011

%e a(4) = 2^1 = 2.

%t CoefficientList[Series[x*(1 + x)*(1 + x^2)/(1 - 2*x^4), {x,0,50}],x] (* or *) Table[2^(Floor[n/4]), {n,0,50}] (* _G. C. Greubel_, Apr 30 2017 *)

%o (PARI) a(n)=2^(n\4) \\ _Charles R Greathouse IV_, Oct 03 2016

%o (Python)

%o def A200675(n): return 1<<(n>>2) # _Chai Wah Wu_, Jan 30 2023

%Y Cf. A000079, A016116, A173862, A108105, A173922, A200678.

%K nonn,easy

%O 0,5

%A _Jeremy Gardiner_, Nov 20 2011

%E Offset corrected by _Charles R Greathouse IV_, Oct 03 2016