login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A197818 Walsh matrix antidiagonals converted to decimal. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 02:24 EST 2014. Contains 250286 sequences.