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 A047237 #40 Sep 08 2022 08:44:56
%S A047237 0,1,2,4,6,7,8,10,12,13,14,16,18,19,20,22,24,25,26,28,30,31,32,34,36,
%T A047237 37,38,40,42,43,44,46,48,49,50,52,54,55,56,58,60,61,62,64,66,67,68,70,
%U A047237 72,73,74,76,78,79,80,82,84,85,86,88,90,91,92,94,96,97
%N A047237 Numbers that are congruent to {0, 1, 2, 4} mod 6.
%C A047237 The sequence is the interleaving of A047238(n) with A016777(n-1). - _Guenther Schrack_, Feb 11 2019
%H A047237 Guenther Schrack, <a href="/A047237/b047237.txt">Table of n, a(n) for n = 1..10002</a>
%H A047237 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%F A047237 Starting (1, 2, 4, 6, ...) = partial sums of (1, 1, 2, 2, 1, 1, 2, 2, ...). - _Gary W. Adamson_, Jun 19 2008
%F A047237 G.f.: x^2*(1+2*x^2) / ((1+x^2)*(1-x)^2). - _R. J. Mathar_, Oct 08 2011
%F A047237 From _Wesley Ivan Hurt_, May 21 2016: (Start)
%F A047237 a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
%F A047237 a(n) = (6*n - 8 + i^(1-n) - i^(1+n))/4 where i=sqrt(-1).
%F A047237 a(2*n) = A016777(n-1), a(2*n-1) = A047238(n). (End)
%F A047237 From _Guenther Schrack_, Feb 11 2019: (Start)
%F A047237 a(n) = (6*n - 8 + (1 - (-1)^n)*(-1)^(n*(n-1)/2))/4.
%F A047237 a(n) = a(n-4) + 6, a(1)=0, a(2)=1, a(3)=2, a(4)=4, for n > 4.
%F A047237 a(-n) = -A047262(n+2).
%F A047237 a(n) = A118286(n-1)/2 for n > 1.
%F A047237 a(n) = A047255(n) - 1. (End)
%F A047237 Sum_{n>=2} (-1)^n/a(n) = sqrt(3)*Pi/36 + log(2)/3 + log(3)/4. - _Amiram Eldar_, Dec 16 2021
%p A047237 A047237:=n->(6*n-8+I^(1-n)-I^(1+n))/4: seq(A047237(n), n=1..100); # _Wesley Ivan Hurt_, May 21 2016
%t A047237 Table[(6n-8+I^(1-n)-I^(1+n))/4, {n, 80}] (* _Wesley Ivan Hurt_, May 21 2016 *)
%t A047237 LinearRecurrence[{2,-2,2,-1},{0,1,2,4},120] (* _Harvey P. Dale_, Jan 21 2018 *)
%o A047237 (Magma) [n : n in [0..110] | n mod 6 in [0, 1, 2, 4]]; // _G. C. Greubel_, Feb 16 2019
%o A047237 (PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(1+2*x^2)/((1+x^2)*(1-x)^2))) \\ _G. C. Greubel_, Feb 16 2019
%o A047237 (Sage) a=(x^2*(1+2*x^2)/((1+x^2)*(1-x)^2)).series(x, 72).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Feb 16 2019
%o A047237 (GAP) Filtered([0..100],n->n mod 6 = 0 or n mod 6 = 1 or n mod 6 = 2 or n mod 6 = 4); # _Muniru A Asiru_, Feb 19 2019
%Y A047237 Cf. A016777, A047238, A047255, A047262, A118286.
%Y A047237 Complement: A047270.
%K A047237 nonn,easy
%O A047237 1,3
%A A047237 _N. J. A. Sloane_
%E A047237 More terms from _Wesley Ivan Hurt_, May 21 2016