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 A060549 #18 Dec 24 2024 13:46:34
%S A060549 0,1,2,2,6,6,12,14,28,28,60,60,120,124,248,248,504,504,1008,1016,2032,
%T A060549 2032,4080,4080,8160,8176,16352,16352,32736,32736,65472,65504,131008,
%U A060549 131008,262080,262080,524160,524224,1048448,1048448,2097024,2097024
%N A060549 a(n) is the number of distinct patterns (modulo geometric D3-operations) with strict median-reflective (palindrome) symmetry (i.e., having no other symmetry) which can be formed by an equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal's triangle modulo 2, where n is the number of cells in each edge of the arrangement. The matching rule is such that any elementary top-down triangle of three neighboring cells in the arrangement contains either one or three white cells.
%H A060549 Harry J. Smith, <a href="/A060549/b060549.txt">Table of n, a(n) for n=1..500</a>
%H A060549 A. Barbé, <a href="http://dx.doi.org/10.1016/S0166-218X(00)00211-0">Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2</a>, Discr. Appl. Math. 105(2000), 1-38.
%H A060549 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A060549 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,0,0,2,0,-4).
%F A060549 a(n) = 2^ceiling(n/2) - 2^(floor((n+3)/6) + d(n)), with d(n)=1 if n mod 6=1 else d(n)=0.
%F A060549 a(n) = A060546(n) - A060548(n) = 2^A008619(n-1) - 2^A008615(n+1), for n >= 1.
%F A060549 G.f.: x^2*(2*x^4 + 2*x^3 + 2*x + 1) / ((2*x^2-1)*(2*x^6-1)). - _Colin Barker_, Aug 29 2013
%o A060549 (PARI) a(n) = { 2^ceil(n/2) - 2^(floor((n + 3)/6) + (n%6==1)) } \\ _Harry J. Smith_, Jul 07 2009
%Y A060549 Cf. A060546, A060548, A008619, A008615.
%K A060549 easy,nonn
%O A060549 1,3
%A A060549 André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001