A197818 Walsh matrix antidiagonals converted to decimal.

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

Offset: 0

Author

Tilman Piesk, Oct 18 2011

Keywords

• nonn
• base

Comments

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.

Examples

			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
		

Links

• Tilman Piesk, Table of n, a(n) for n = 0..1023
• Tilman Piesk, Negated binary Walsh matrix of size 256
• Tilman Piesk, The antidiagonals shown in a triangular matrix
• Wikipedia, Walsh matrix

Crossrefs

Cf. A001317, A099627.

Programs

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))
/* Joerg Arndt, Mar 27 2013 */