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 A229154 #22 Feb 01 2022 07:11:55
%S A229154 1,2,5,8,12,16,21,27,33,40,48,56,65,75,85,96,108,120,133,147,161,176,
%T A229154 192,208,225,243,261,280,300,320,341,363,385,408,432,456,481,507,533,
%U A229154 560,588,616,645,675,705,736,768,800,833,867,901,936,972,1008,1045
%N A229154 The clubs patterns appearing in n X n coins, with rotation allowed.
%C A229154 On the Japanese TV show "Tsuki no Koibito", a girl told her boyfriend that she saw a heart in 4 coins. Actually there are a total of 6 distinct patterns appearing in 2 X 2 coins in which each pattern consists of a part of the perimeter of each coin and forms a continuous area.
%C A229154 a(n) is the number of clubs patterns appearing in n X n coins with rotation allowed. It is also A000212, except for the fourth term. The number of inverse patterns (stars or voids between clubs) is A143978 (except for the first term).
%H A229154 Vincenzo Librandi, <a href="/A229154/b229154.txt">Table of n, a(n) for n = 2..1000</a>
%H A229154 Kival Ngaokrajang, <a href="/A229154/a229154.pdf">Illustration of initial terms</a>
%H A229154 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A229154 a(n) = floor(n^2/3), a(3) = 2.
%F A229154 From _Colin Barker_, Oct 08 2013: (Start)
%F A229154 a(n) = n^2/3 + (2/9)*cos((2*Pi*n)/3) - 2/9.
%F A229154 G.f.: -x^2*(x^6-2*x^5+x^4-x^3+2*x^2+1) / ((x-1)^3*(x^2+x+1)). (End)
%t A229154 CoefficientList[Series[-(x^6 - 2 x^5 + x^4 - x^3 + 2 x^2 + 1)/((x - 1)^3 (x^2 + x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 08 2013 *)
%o A229154 (PARI) Vec(-x^2*(x^6-2*x^5+x^4-x^3+2*x^2+1)/((x-1)^3*(x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Oct 08 2013
%Y A229154 Cf. A000212, A143978, A074148 (Heart patterns), A227906, A229093 (Clubs pattern, fixed Orientation).
%K A229154 nonn,easy
%O A229154 2,2
%A A229154 _Kival Ngaokrajang_, Sep 15 2013
%E A229154 More terms from _Colin Barker_, Oct 08 2013