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.

0, 1, 2, 2, 6, 6, 12, 14, 28, 28, 60, 60, 120, 124, 248, 248, 504, 504, 1008, 1016, 2032, 2032, 4080, 4080, 8160, 8176, 16352, 16352, 32736, 32736, 65472, 65504, 131008, 131008, 262080, 262080, 524160, 524224, 1048448, 1048448, 2097024, 2097024

Offset

1,3

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 sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,0,2,0,-4).

Formula

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.

a(n) = A060546(n) - A060548(n) = 2^A008619(n-1) - 2^A008615(n+1), for n >= 1.

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

Prog

(PARI) a(n) = { 2^ceil(n/2) - 2^(floor((n + 3)/6) + (n%6==1)) } \\ Harry J. Smith, Jul 07 2009

Crossrefs

Cf. A060546, A060548, A008619, A008615.

Sequence in context: A332759 A139550 A337735 * A228315 A120690 A165124

Adjacent sequences: A060546 A060547 A060548 * A060550 A060551 A060552

Keyword

easy,nonn,changed

Author

André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001

Status

approved