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 A241807 #12 May 03 2014 12:02:46
%S A241807 1,1,2,7,11,2,11,29,37,23,28,67,79,23,53,121,137,77,86,191,211,29,127,
%T A241807 277,301,163,176,379,407,109,233,497,529,281,298,631,667,88,371,781,
%U A241807 821,431,452,947,991,259,541,1129,1177,613,638
%N A241807 Numerators of c(n) = (n^2+n+2)/((n+1)*(n+2)*(n+3)) as defined in A241269.
%C A241807 The subsequence 1, 23, 77, 163, 281, 431, 613, 827, ..., with indices congruent to 1 mod 8, is 16n^2+6n+1, that is, A000124(8n+1)/2 or A014206(8n+1)/4. Its second differences are constant: (16n^2+6n+1)'' = 32.
%C A241807 The sequence A014206/A241807 is integral and consists of the 16-periodic sequence (2, 4, 4, 2, 2, 16, 4, 2, 2, 4, 4, 2, 2, 8, 4, 2, ...).
%F A241807 a(n) = A014206(n)/period 16: repeat 2, 4, 4, 2, 2, 16, 4, 2, 2, 4, 4, 2, 2, 8, 4, 2 (conjectured).
%F A241807 a(4k) = 8*k^2 +2*k +1,
%F A241807 a(4k+2) = 4*k^2 +5*k +2,
%F A241807 a(4k+3) = 8*k^2 +14*k +7,
%F A241807 a(8k+1) = 16*k^2 +6*k +1,
%F A241807 a(16k+5) = 16*k^2 +11*k +2,
%F A241807 a(16k+13) = 32*k^2 + 54*k +23.
%e A241807 1/3, 1/6, 2/15, 7/60, 11/105, 2/21, 11/126, 29/360, 37/495, 23/330, ...
%t A241807 Table[(n^2+n+2)/((n+1)*(n+2)*(n+3)) // Numerator, {n, 0, 50}]
%Y A241807 Cf. A000124, A014206, A241269, A188135, A054552, A185438.
%K A241807 nonn,frac
%O A241807 0,3
%A A241807 _Jean-François Alcover_ and _Paul Curtz_, Apr 29 2014