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%I #38 Mar 29 2014 02:42:26
%S 1,3,5,15,17,51,93,255,257,771,1453,3855,4593,13299,23901,65535,65537,
%T 196611,371373,983055,1175281,3394803,6103645,16711935,16908033,
%U 50593539,95245741,252706575,301011441,871576563,1566432605,4294967295
%N Walsh matrix antidiagonals converted to decimal.
%C Infinite Walsh matrix with the negative ones replaced by zeros (negated binary Walsh matrix), the antidiagonals read as binary numbers.
%C 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.
%H Tilman Piesk, <a href="/A197818/b197818.txt">Table of n, a(n) for n = 0..1023</a>
%H Tilman Piesk, <a href="http://commons.wikimedia.org/wiki/File:Binary_Walsh_matrix_256_neg.svg">Negated binary Walsh matrix of size 256</a>
%H Tilman Piesk, <a href="http://commons.wikimedia.org/wiki/File:Binary_Walsh_matrix_256_neg;_diags_to_cols.svg">The antidiagonals shown in a triangular matrix</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Walsh_matrix">Walsh matrix</a>
%e Top left corner of the negated binary Walsh matrix:
%e 1 1 1 1 1 1 1 1
%e 1 0 1 0 1 0 1 0
%e 1 1 0 0 1 1 0 0
%e 1 0 0 1 1 0 0 1
%e 1 1 1 1 0 0 0 0
%e 1 0 1 0 0 1 0 1
%e 1 1 0 0 0 0 1 1
%e 1 0 0 1 0 1 1 0
%e The antidiagonals in binary and decimal are:
%e 1 = 1
%e 11 = 3
%e 101 = 5
%e 1111 = 15
%e 10001 = 17
%e 110011 = 51
%e 1011101 = 93
%e 11111111 = 255
%o (PARI)
%o N=2^5; /* a power of 2 */
%o parity(x)= {
%o my(s=1);
%o while ( (x>>s), x=bitxor(x, x>>s); s+=s; );
%o return( bitand(x,1) );
%o }
%o W = matrix(N,N, i,j, if(parity(bitand(i-1,j-1)),0,1); );
%o a(n) = sum(k=0,n, 2^k * W[n-k+1,k+1] );
%o vector(N,n,a(n-1))
%o /* _Joerg Arndt_, Mar 27 2013 */
%Y Cf. A001317, A099627.
%K nonn,base
%O 0,2
%A _Tilman Piesk_, Oct 18 2011
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