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%I #27 Oct 16 2023 11:13:33
%S 1,7,30,121,487,1950,7801,31207,124830,499321,1997287,7989150,
%T 31956601,127826407,511305630,2045222521,8180890087,32723560350,
%U 130894241401,523576965607,2094307862430,8377231449721,33508925798887,134035703195550,536142812782201,2144571251128807
%N Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,2.
%H Paolo Xausa, <a href="/A037611/b037611.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,1,-4).
%F From _R. J. Mathar_, Apr 27 2015: (Start)
%F G.f.: x*(1+x)*(2*x+1) / ( (x-1)*(4*x-1)*(1+x+x^2) ).
%F A007090(a(n)) = A037617(n). (End)
%F a(n) ~ (10/21)*4^n = (10/21)*A000302(n). - _Stefano Spezia_, Oct 15 2023
%t LinearRecurrence[{4,0,1,-4},{1,7,30,121},30] (* _Paolo Xausa_, Oct 16 2023 *)
%o (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -4,1,0,4]^(n-1)*[1;7;30;121])[1,1] \\ _Charles R Greathouse IV_, Feb 13 2017
%Y Cf. A000302, A007090, A037617.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_
%E a(24)-a(26) from _Stefano Spezia_, Oct 15 2023
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