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A305859 Numbers that are congruent to {1, 3, 11} mod 12.

%I A305859 #57 Mar 15 2023 20:17:57
%S A305859 1,3,11,13,15,23,25,27,35,37,39,47,49,51,59,61,63,71,73,75,83,85,87,
%T A305859 95,97,99,107,109,111,119,121,123,131,133,135,143,145,147,155,157,159,
%U A305859 167,169,171,179,181,183,191,193,195,203,205,207,215,217,219,227,229,231,239
%N A305859 Numbers that are congruent to {1, 3, 11} mod 12.
%H A305859 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A305859 G.f.: x*(1 + 2*x + 8*x^2 + x^3)/((1 - x)^2*(1 + x + x^2)).
%F A305859 a(n) = a(n-1) + a(n-3) - a(n-4) for n>12.
%F A305859 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) for n>6.
%F A305859 a(n) = 2*n + 6*floor(n/3) - 1. - _Bruno Berselli_, Jun 13 2018
%t A305859 Table[2 n + 6 Floor[n/3] - 1, {n, 1, 60}] (* _Bruno Berselli_, Jun 13 2018 *)
%t A305859 LinearRecurrence[{1,0,1,-1},{1,3,11,13},60] (* _Harvey P. Dale_, Mar 15 2023 *)
%o A305859 (Magma) [n: n in [0..300] | n mod 12 in [1,3,11]]; // _Bruno Berselli_, Jun 13 2018
%Y A305859 Equals 2*A047240 - 1 and 2*A047266 + 1 (after 0).
%K A305859 nonn,easy,less
%O A305859 1,2
%A A305859 _Vincenzo Librandi_, Jun 12 2018
%E A305859 Edited by _Bruno Berselli_, Jun 13 2018