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 A060551 #24 Dec 24 2024 13:46:30
%S A060551 0,0,0,6,12,42,84,210,420,924,1860,3900,7800,15996,31992,64728,129528,
%T A060551 260568,521136,1045464,2090928,4187952,8376240,16764720,33529440,
%U A060551 67084080,134168160,268385376,536772192,1073642592,2147285184,4294769760,8589539520,17179472064
%N A060551 a(n) is the number of nonsymmetric patterns (no reflective, nor rotational symmetry) which may 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 A060551 Harry J. Smith, <a href="/A060551/b060551.txt">Table of n, a(n) for n=1..500</a>
%H A060551 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 A060551 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A060551 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2,-4,-4,10,-4,-4,4,8,8,-16).
%F A060551 a(n) = 2^n - 3*2^ceiling(n/2) - 2^(floor(n/3)+(n mod 3)mod 2) + 3*2^(floor((n+3)/6) + d(n)), with d(n)=1 if n mod 6=1 else d(n)=0.
%F A060551 a(n) = A000079(n) - 3*A060546(n) - A060547(n) + 3*A060548(n).
%F A060551 a(n) = A000079(n) - 3*2^A008619(n-1) - 2^A008611(n-1) + 3*2^A008615(n+1), for n >= 1.
%F A060551 G.f.: -6*x^4*(2*x^6 + 2*x^5 - x^4 + 2*x^3 - x^2 - 1) / ((2*x-1)*(2*x^2-1)*(2*x^3-1)*(2*x^6-1)). - _Colin Barker_, Aug 29 2013
%F A060551 a(n) = 6*A060552(n). - _Andrew Howroyd_, Dec 24 2024
%t A060551 LinearRecurrence[{2,2,-2,-4,-4,10,-4,-4,4,8,8,-16},{0,0,0,6,12,42,84,210,420,924,1860,3900},40] (* _Harvey P. Dale_, Feb 01 2015 *)
%o A060551 (PARI) a(n) = { 2^n-3*2^ceil(n/2)-2^(floor(n/3)+(n%3)%2)+3*2^(floor((n+3)/6)+(n%6==1)) } \\ _Harry J. Smith_, Jul 07 2009
%Y A060551 Cf. A000079, A060546, A060547, A060548, A008619, A008611, A008615.
%K A060551 easy,nonn
%O A060551 1,4
%A A060551 André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001
%E A060551 More terms from _Colin Barker_, Aug 29 2013