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A197818 Walsh matrix antidiagonals converted to decimal.

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