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A211344 Atomic Boolean functions interpreted as binary numbers. 2
1, 3, 5, 15, 51, 85, 255, 3855, 13107, 21845, 65535, 16711935, 252645135, 858993459, 1431655765, 4294967295, 281470681808895, 71777214294589695, 1085102592571150095, 3689348814741910323, 6148914691236517205 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row n of the triangle shows the atoms among n-ary Boolean functions:

            1                                  01

         3     5                       0011          0101

     15    51     85          00001111      00110011      01010101

Often n-ary x_k = T(n,k), e.g. for 2-ary functions x_1=0011, x_2=0101 and for 3-ary functions x_1=00001111, x_2=00110011, x_3=01010101.

An easier generalized way is the enumeration from right to left (preferably from x_0) so that n-ary x_k = T(n,n-k). As numbers in the diagonals on the right have the same bit pattern this goes well together with the infinitary definition of atomic formulas as x_k = 1/A000215(k) = 1/(2^2^k+1) in binary:

2-ary x_0=0101=5, 3-ary x_0=01010101=85, infinitary x_0=1/3=.010101...

2-ary x_1=0011=3, 3-ary x_1=00110011=51, infinitary x_1=1/5=.001100110011...

LINKS

Tilman Piesk, Table of n, a(n) for n = 0..65

Tilman Piesk, Atomic Boolean functions in Sierpinski triangle (Wikimedia Commons)

FORMULA

a = A001317( A089633 )

PROG

(Matlab)

Seq = sym(zeros(55, 1)) ;

Filledlines = 0 ;

for m=1:10

    for n=1:m

        Sum = sym(0) ;

        for k=0:2^m-1

            if mod(  floor( k/2^(m-n) )  , 2) == 0

               Sum = Sum + 2^sym(k) ;

            end

        end

        Seq( Filledlines + n ) = Sum ;

    end

    Filledlines = Filledlines + m ;

end

CROSSREFS

A001317, A089633, A051179 (left diagonal)

Sequence in context: A103043 A018601 A190733 * A006394 A018650 A177814

Adjacent sequences:  A211341 A211342 A211343 * A211345 A211346 A211347

KEYWORD

nonn,tabl

AUTHOR

Tilman Piesk, Jul 24 2012

STATUS

approved

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Last modified December 21 05:22 EST 2014. Contains 252296 sequences.