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A039301 Number of distinct quadratic residues mod 4^n.

%I A039301 #33 Jan 29 2025 06:58:14
%S A039301 1,2,4,12,44,172,684,2732,10924,43692,174764,699052,2796204,11184812,
%T A039301 44739244,178956972,715827884,2863311532,11453246124,45812984492,
%U A039301 183251937964,733007751852,2932031007404,11728124029612,46912496118444,187649984473772,750599937895084
%N A039301 Number of distinct quadratic residues mod 4^n.
%C A039301 Number of distinct n-digit suffixes of base 4 squares.
%H A039301 Vincenzo Librandi, <a href="/A039301/b039301.txt">Table of n, a(n) for n = 0..170</a>
%H A039301 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F A039301 a(n) = floor((4^n+10)/6).
%F A039301 a(n) = A007583(n-1)+1 = A020988(n-2)+2 = A083584(n-2)+3. - _Ralf Stephan_, Jun 14 2003
%F A039301 Also, a(0)=1 and, for n>0, a(n) = (4^n+8)/6. - _Bruno Berselli_, Jul 27 2010
%F A039301 G.f.: (1-3*x-2*x^2)/((1-x)*(1-4*x)). - _Bruno Berselli_, Jul 27 2010
%F A039301 a(n)-5*a(n-1)+4*a(n-2) = 0 for n>1. - _Bruno Berselli_, Jul 27 2010
%t A039301 Floor[(4^Range[0, 30] + 10)/6] (* _Paolo Xausa_, Jan 29 2025 *)
%o A039301 (Magma) [Floor((4^n+10)/6): n in [0..40] ]; // _Vincenzo Librandi_, Apr 28 2011
%K A039301 nonn,easy
%O A039301 0,2
%A A039301 _David W. Wilson_