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A213173 a(n) = 4^floor(n/2), Powers of 4 repeated.

%I A213173 #37 Jun 04 2025 16:23:23
%S A213173 1,1,4,4,16,16,64,64,256,256,1024,1024,4096,4096,16384,16384,65536,
%T A213173 65536,262144,262144,1048576,1048576,4194304,4194304,16777216,
%U A213173 16777216,67108864,67108864,268435456,268435456,1073741824,1073741824,4294967296,4294967296
%N A213173 a(n) = 4^floor(n/2), Powers of 4 repeated.
%C A213173 1, followed by A056450. - _Joerg Arndt_, Sep 17 2013
%C A213173 Binomial transform of A084567.
%C A213173 Unsigned version of A164111.
%C A213173 Also, number of walks of length n on the star S_4 = K_1,4 starting at a specific vertex of degree 1. - _Sean A. Irvine_, Jun 03 2025
%H A213173 G. C. Greubel, <a href="/A213173/b213173.txt">Table of n, a(n) for n = 0..1000</a>
%H A213173 Sean A. Irvine, <a href="https://oeis.org/wiki/User:Sean_A._Irvine/Walks_on_Graphs#5_vertices">Walks on Graphs</a>.
%H A213173 Wikipedia, <a href="https://en.wikipedia.org/wiki/Star_(graph_theory)">Star (graph theory)</a>
%H A213173 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4).
%F A213173 O.g.f.: (1+x)/(1-4*x^2).
%F A213173 a(n) = A016116(n)^2.
%F A213173 a(n) = 4*a(n-2) with a(0) = a(1) = 1.
%F A213173 a(n) = a(n-1)*a(n-2)/a(n-3) = 4^A004526(n).
%F A213173 a(n) = sum(A152815(n,k)*3^k, 0<=k<=n). - _Philippe Deléham_, Apr 22 2013
%t A213173 LinearRecurrence[{0, 4}, {1, 1}, 40] (* _T. D. Noe_, Apr 17 2013 *)
%t A213173 CoefficientList[Series[(1 + x)/(1 - 4*x^2), {x,0,50}], x] (* _G. C. Greubel_, Apr 30 2017 *)
%t A213173 With[{p4=4^Range[0,30]},Riffle[p4,p4]] (* _Harvey P. Dale_, Mar 17 2022 *)
%o A213173 (PARI) a(n)=4^(n\2) \\ _Charles R Greathouse IV_, Oct 03 2016
%Y A213173 Cf. A000302, A056450, A164111.
%K A213173 nonn,easy
%O A213173 0,3
%A A213173 _Philippe Deléham_, Apr 14 2013