This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047250 #36 Sep 08 2022 08:44:56
%S A047250 0,3,4,5,6,9,10,11,12,15,16,17,18,21,22,23,24,27,28,29,30,33,34,35,36,
%T A047250 39,40,41,42,45,46,47,48,51,52,53,54,57,58,59,60,63,64,65,66,69,70,71,
%U A047250 72,75,76,77,78,81,82,83,84,87,88,89,90,93,94,95,96,99
%N A047250 Numbers that are congruent to {0, 3, 4, 5} (mod 6).
%C A047250 The sequence is the interleaving of A047233 with A047270. - _Guenther Schrack_, Feb 15 2019
%H A047250 Guenther Schrack, <a href="/A047250/b047250.txt">Table of n, a(n) for n = 1..10010</a>
%H A047250 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047250 G.f.: x^2*(3+x+x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2). - _R. J. Mathar_, Oct 08 2011
%F A047250 From _Wesley Ivan Hurt_, Jun 02 2016: (Start)
%F A047250 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047250 a(n) = (6*n - 3 + i^(2*n) - (1+i)*i^(-n) - (1-i)*i^n)/4 where i=sqrt(-1).
%F A047250 a(2*k) = A047270(k), a(2*k-1) = A047233(k). (End)
%F A047250 E.g.f.: (2 - sin(x) - cos(x) + (3*x - 2)*sinh(x) + (3*x - 1)*cosh(x))/2. - _Ilya Gutkovskiy_, Jun 02 2016
%F A047250 From _Guenther Schrack_, Feb 15 2019: (Start)
%F A047250 a(n) = (6*n - 3 + (-1)^n - 2*(-1)^(n*(n-1)/2))/4.
%F A047250 a(n) = a(n-4) + 6, a(1)=0, a(2)=3, a(3)=4, a(4)=5, for n > 4.
%F A047250 a(-n) = -A047246(n+2). (End)
%F A047250 Sum_{n>=2} (-1)^n/a(n) = 2*log(2)/3 - Pi/(6*sqrt(3)). - _Amiram Eldar_, Dec 17 2021
%p A047250 A047250:=n->(6*n-3+I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/4: seq(A047250(n), n=1..100); # _Wesley Ivan Hurt_, Jun 02 2016
%t A047250 Select[Range[0,100], MemberQ[{0,3,4,5}, Mod[#,6]]&] (* or *) LinearRecurrence[{1,0,0,1,-1}, {0,3,4,5,6}, 60] (* _Harvey P. Dale_, Apr 01 2013 *)
%o A047250 (Magma) [n : n in [0..150] | n mod 6 in [0, 3, 4, 5]]; // _Wesley Ivan Hurt_, Jun 02 2016
%o A047250 (PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(3+x+x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2))) \\ _G. C. Greubel_, Feb 16 2019
%o A047250 (Sage) a=(x^2*(3+x+x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2)).series(x, 72).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Feb 16 2019
%Y A047250 Cf. A047233, A047246, A047270.
%Y A047250 Complement: A047239.
%K A047250 nonn,easy
%O A047250 1,2
%A A047250 _N. J. A. Sloane_