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A197818
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Walsh matrix antidiagonals converted to decimal.
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3
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1, 3, 5, 15, 17, 51, 93, 255, 257, 771, 1453, 3855, 4593, 13299, 23901, 65535, 65537, 196611, 371373, 983055, 1175281, 3394803, 6103645, 16711935, 16908033, 50593539, 95245741, 252706575, 301011441, 871576563, 1566432605, 4294967295
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OFFSET
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0,2
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COMMENTS
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Infinite Walsh matrix with the negative ones replaced by zeros (negated binary Walsh matrix), the antidiagonals read as binary numbers.
This sequence is similar to A001317 (Sierpinski triangle rows converted to decimal). a(n) = A001317(n) iff n=0 or n is an element of A099627.
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LINKS
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EXAMPLE
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Top left corner of the negated binary Walsh matrix:
1 1 1 1 1 1 1 1
1 0 1 0 1 0 1 0
1 1 0 0 1 1 0 0
1 0 0 1 1 0 0 1
1 1 1 1 0 0 0 0
1 0 1 0 0 1 0 1
1 1 0 0 0 0 1 1
1 0 0 1 0 1 1 0
The antidiagonals in binary and decimal are:
1 = 1
11 = 3
101 = 5
1111 = 15
10001 = 17
110011 = 51
1011101 = 93
11111111 = 255
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PROG
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(PARI)
N=2^5; /* a power of 2 */
parity(x)= {
my(s=1);
while ( (x>>s), x=bitxor(x, x>>s); s+=s; );
return( bitand(x, 1) );
}
W = matrix(N, N, i, j, if(parity(bitand(i-1, j-1)), 0, 1); );
a(n) = sum(k=0, n, 2^k * W[n-k+1, k+1] );
vector(N, n, a(n-1))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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