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

0,2

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.

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

Example

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

Prog

(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 */

Crossrefs

Cf. A001317, A099627.

Sequence in context: A045544 A001317 A053576 * A077406 A054432 A016043

Adjacent sequences: A197815 A197816 A197817 * A197819 A197820 A197821

Keyword

nonn,base

Author

Tilman Piesk, Oct 18 2011

Status

approved