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 A087444 #54 Aug 20 2022 18:24:46
%S A087444 1,4,10,13,19,22,28,31,37,40,46,49,55,58,64,67,73,76,82,85,91,94,100,
%T A087444 103,109,112,118,121,127,130,136,139,145,148,154,157,163,166,172,175,
%U A087444 181,184,190,193,199,202,208,211,217,220,226,229,235,238,244,247,253
%N A087444 Numbers that are congruent to {1, 4} mod 9.
%C A087444 3*a(n) is conjectured to be the total number of sides (straight double bonds (long side) and single bond (short side)) of a certain equilateral triangle expansion shown in one of the links. The pattern is supposed to become the planar Archimedean net 3.3.3.3.6 when n -> infinity. 3*a(n) is also conjectured to be the total number of sided (bonds) in another version of an equilateral triangle expansion that is supposed to become the planar Archimedean net 3.6.3.6. See the illustrations in the links. - _Kival Ngaokrajang_, Nov 30 2014
%H A087444 David Lovler, <a href="/A087444/b087444.txt">Table of n, a(n) for n = 1..10000</a>
%H A087444 Kival Ngaokrajang, <a href="/A087444/a087444.pdf">Illustration of initial terms (3.3.3.3.6)</a>, <a href="/A087444/a087444_1.pdf">(3.6.3.6)</a>
%H A087444 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A087444 G.f.: x*(1+3*x+5*x^2)/((1+x)*(1-x)^2).
%F A087444 E.g.f.: 5 + ((9*x - 17/2)*exp(x) - (3/2)*exp(-x))/2.
%F A087444 a(n) = (18*n - 17 - 3*(-1)^n)/4.
%F A087444 a(n) = 9*n - a(n-1) - 13 (with a(1)=1). - _Vincenzo Librandi_, Aug 08 2010
%t A087444 Select[Range[300],MemberQ[{1,4},Mod[#,9]]&] (* or *) LinearRecurrence[ {1,1,-1},{1,4,10},60] (* _Harvey P. Dale_, Jan 22 2019 *)
%o A087444 (PARI) a(n) = (18*n - 17 - 3*(-1)^n)/4 \\ _David Lovler_, Aug 20 2022
%Y A087444 Cf. A001651, A047241, A087445, A087446.
%K A087444 easy,nonn
%O A087444 1,2
%A A087444 _Paul Barry_, Sep 04 2003
%E A087444 _Kival Ngaokrajang_'s comment reworded by _Wolfdieter Lang_, Dec 05 2014
%E A087444 E.g.f. and formula adapted to offset by _David Lovler_, Aug 20 2022