This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 1
 0, 0, 0, 6, 12, 42, 84, 210, 420, 924, 1860, 3900, 7800, 15996, 31992, 64728, 129528, 260568, 521136, 1045464, 2090928, 4187952, 8376240, 16764720, 33529440, 67084080, 134168160, 268385376, 536772192, 1073642592, 2147285184, 4294769760, 8589539520, 17179472064 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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. Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-4,-4,10,-4,-4,4,8,8,-16). FORMULA 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. a(n) = A000079(n) - 3*A060546(n) - A060547(n) + 3*A060548(n). a(n) = A000079(n) - 3*2^A008619(n-1) - 2^A008611(n-1) + 3*2^A008615(n+1), for n >= 1. 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 MATHEMATICA 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 *) PROG (PARI) { for (n=1, 500, a=2^n-3*2^ceil(n/2)-2^(floor(n/3)+(n%3)%2)+3*2^(floor((n+3)/6)+(n%6==1)); write("b060551.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 07 2009 CROSSREFS Cf. A000079, A060546, A060547, A060548, A008619, A008611, A008615. Sequence in context: A206039 A048069 A152787 * A129113 A048025 A120471 Adjacent sequences:  A060548 A060549 A060550 * A060552 A060553 A060554 KEYWORD easy,nonn AUTHOR André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001 EXTENSIONS More terms from Colin Barker, Aug 29 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 19 12:21 EDT 2019. Contains 328220 sequences. (Running on oeis4.)