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A223541 Matrix T(m,n) = nim-product(2^m,2^n) read by antidiagonals. 7
1, 2, 2, 4, 3, 4, 8, 8, 8, 8, 16, 12, 6, 12, 16, 32, 32, 11, 11, 32, 32, 64, 48, 64, 13, 64, 48, 64, 128, 128, 128, 128, 128, 128, 128, 128, 256, 192, 96, 192, 24, 192, 96, 192, 256, 512, 512, 176, 176, 44, 44, 176, 176, 512, 512, 1024, 768 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Nimber multiplication is commutative, so this array is symmetric, and can be represented in a more compact way by the rows of the lower triangle (A223540).

The diagonal is A006017 (nim-squares of powers of 2).

The elements of this array are listed in A223543. In the key-matrix A223542 the entries of this array (which become very large) are replaced by the corresponding index numbers of A223543. (Surprisingly, the key-matrix seems to be interesting on its own.)

The number of different entries per antidiagonal is probably A002487. That would mean, there are exactly A002487(n+1) numbers that can be expressed as a nim-product(2^a,2^b) with a+b=n. - Tilman Piesk, Mar 27 2013

LINKS

Tilman Piesk, First 128 rows of the matrix, flattened

Tilman Piesk, Elements of dual matrix (256 SVGs)

Tilman Piesk, Walsh permutation; nimber multiplication (Wikiversity)

Tilman Piesk, Class bin and function nimprod (Matlab code)

FORMULA

a(m,n) = A051775(A000079(m),A000079(n)).

a(m,n) = A223543(A223542(m,n)).

EXAMPLE

a(1,7) = a(3,5) = 192, the result of the nim-multiplications 2^1*2^7 and 2^3*2^5.

PROG

(Matlab, see code linked above)

A = bin([256 256], 'pre') ;

for m=1:256

    for n=1:m

        a = nimprod( bin(m-1) , bin(n-1) ) ;

        A(m, n) = a ;

        A(n, m) = a ;

    end

end

CROSSREFS

Cf. A051775, A223540, A006017, A223543, A223542, A000079, A002487.

Sequence in context: A157927 A227256 A131816 * A128181 A125185 A173387

Adjacent sequences:  A223538 A223539 A223540 * A223542 A223543 A223544

KEYWORD

nonn,tabl

AUTHOR

Tilman Piesk, Mar 21 2013

STATUS

approved

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Last modified December 20 22:17 EST 2014. Contains 252289 sequences.