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 A060552 a(n) is the number of distinct (modulo geometric D3-operations) nonsymmetric (no reflective nor rotational symmetry) patterns 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. 1
 0, 0, 0, 1, 2, 7, 14, 35, 70, 154, 310, 650, 1300, 2666, 5332, 10788, 21588, 43428, 86856, 174244, 348488, 697992, 1396040, 2794120, 5588240, 11180680, 22361360, 44730896, 89462032, 178940432, 357880864, 715794960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Harry J. Smith, Table of n, a(n) for n=1..500 A. Barbé, Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2, Discr. Appl. Math. 105(2000), 1-38. FORMULA a(n) = (2^(n-1) - 2^(floor(n/3) + (n mod 3)mod 2 - 1))/3 + 2^(floor((n+3)/6) + d(n) - 1) - 2^floor((n-1)/2), with d(n)=1 if n mod 6=1 else d(n)=0. a(n) = (A000079(n-1) - A060547(n)/2)/3 + A060548(n)/2 -A060546(n)/2. a(n) = (A000079(n-1) - 2^(A008611(n-1) - 1))/3 + 2^(A008615(n+1) - 1) - 2^(A008619(n-1) - 1), n >= 1. From R. J. Mathar, Aug 03 2009: (Start) a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) - 4*a(n-4) - 4*a(n-5) + 10*a(n-6) - 4*a(n-7) - 4*a(n-8) + 4*a(n-9) + 8*a(n-10) + 8*a(n-11) - 16*a(n-12). G.f.: -x^4*(-1 - x^2 - x^4 + 2*x^3 + 2*x^5 + 2*x^6)/((2*x-1)*(2*x^2-1)*(2*x^3-1)*(2*x^6-1)). (End) PROG (PARI) { for (n=1, 500, a=(2^(n-1)-2^(floor(n/3)+(n%3)%2-1))/3+2^(floor((n+3)/6)+(n%6==1)-1)-2^floor((n-1)/2); write("b060552.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 07 2009 CROSSREFS Cf. A000079, A060547, A060548, A060546, A060552, A008611, A008615, A008619. Sequence in context: A128902 A227213 A319455 * A274868 A191396 A173126 Adjacent sequences:  A060549 A060550 A060551 * A060553 A060554 A060555 KEYWORD easy,nonn AUTHOR André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001 STATUS approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)