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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. 1
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: A084202 A053637 A000016 * A032307 A007560 A032237

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

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Last modified July 27 04:52 EDT 2017. Contains 289841 sequences.