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%I #24 Apr 16 2021 15:41:28
%S 0,4,20,72,280,1040,4200,16408,65840,262296,1049680,4194344,16782000,
%T 67108912,268451960,1073744160,4295033440,17179869248,68719747320,
%U 274877907016,1099512679520,4398046544304,17592190238920,70368744177752
%N a(n) = Sum_{d|n} phi(d)*4^(n/d).
%H Seiichi Manyama, <a href="/A054611/b054611.txt">Table of n, a(n) for n = 0..1660</a>
%H T. Pisanski, D. Schattschneider and B. Servatius, <a href="http://www.jstor.org/stable/27642932">Applying Burnside's lemma to a one-dimensional Escher problem</a>, Math. Mag., 79 (2006), 167-180. See V(n).
%F a(n) = n * A001868(n).
%F a(n) = Sum_{k=1..n} 4^gcd(n,k). - _Ilya Gutkovskiy_, Apr 16 2021
%p A054611:=proc(n) local k, t1; t1:=0; for k in divisors(n) do t1 := t1+phi(k)*4^(n/k); od: t1; end;
%o (PARI) a(n) = if(n==0, 0, sumdiv(n, d, eulerphi(d)*4^(n/d))); \\ _Michel Marcus_, Sep 19 2017
%Y Column k=4 of A185651.
%Y Row n=4 of A054619.
%Y Cf. A001868.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Apr 16 2000
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