Java (OpenJDK 9), 188 bytes
n->{for(int s=(int)Math.pow(3,n),x=0,y;x<s;x++)for(y=0;y<=s;y++)System.out.print(y==s?'\n':h(s,x,y)<1?' ':'H');} int h(int s,int x,int y){return s>3?h(s/=3,x/3,y/3)&h(s,x%s,y%s):++y%2|x%2;} Olivier Grégoire
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