A060553 - OEIS

A060553

a(n) is the number of distinct (modulo geometric D3-operations) 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.

2, 2, 4, 6, 10, 16, 32, 52, 104, 192, 376, 720, 1440, 2800, 5600, 11072, 22112, 43968, 87936, 175296, 350592, 700160, 1400192, 2798336, 5596672, 11188992, 22377984, 44747776, 89495040, 178973696, 357947392, 715860992, 1431721984, 2863378432, 5726754816

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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 (2,2,-2,-4,-4,8).

FORMULA

a(n) = (2^(n-1)+2^(floor(n/3) + (n mod 3)mod 2))/3 + 2^floor((n-1)/2).

a(n) = (A000079(n-1) + A060547(n))/3 + A060546(n)/2.

a(n) = (A000079(n-1) + 2^A008611(n-1))/3 + 2^(A008619(n-1) - 1), for n >= 1.

G.f.: -2*x*(4*x^5 + x^4 - x^3 - 2*x^2 - x + 1) / ((2*x-1)*(2*x^2-1)*(2*x^3-1)). - Colin Barker, Aug 29 2013

PROG

(PARI) { for (n=1, 500, a=(2^(n-1) + 2^(floor(n/3) + (n%3)%2))/3 + 2^floor((n-1)/2); write("b060553.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 07 2009

CROSSREFS

Cf. A000079, A060547, A060546, A008611, A008619.

Sequence in context: A053637 A000016 A361223 * A293673 A344707 A293505

Adjacent sequences: A060550 A060551 A060552 * A060554 A060555 A060556

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