A195916 Table with T(n,n) = n, T(n,k) = xor(T(n-1,k-1), T(n-1,k))

1, 1, 2, 1, 3, 3, 1, 2, 0, 4, 1, 3, 2, 4, 5, 1, 2, 1, 6, 1, 6, 1, 3, 3, 7, 7, 7, 7, 1, 2, 0, 4, 0, 0, 0, 8, 1, 3, 2, 4, 4, 0, 0, 8, 9, 1, 2, 1, 6, 0, 4, 0, 8, 1, 10, 1, 3, 3, 7, 6, 4, 4, 8, 9, 11, 11, 1, 2, 0, 4, 1, 2, 0, 12, 1, 2, 0, 12

Offset

1,3

Comments

We take T(n,0) = 0 for the calculation.

Every column is periodic. It appears that, if 2^j > k, column k has period 2^j. If so, then for j >= i, T(2^j,2^i) = 2^i and T(2^j,k) = 0 if k is not a power of 2.

Links

Table of n, a(n) for n=1..78.

Example

The table starts:
1
1, 2
1, 3, 3
1, 2, 0, 4
1, 3, 2, 4, 5
1, 2, 1, 6, 1, 6
1, 3, 3, 7, 7, 7, 7

Prog

(PARI) anrow(n)=local(r, v); r=v=[1]; for(k=2, n, v=vector(#v+1, j, if(j==k, k, bitxor(v[j], if(j==1, 0, v[j-1])))); r=concat(r, v)); r

Crossrefs

Row reversals of A195915. For xor see A003987.

Sequence in context: A274309 A158440 A119803 * A245554 A110569 A140815

Adjacent sequences: A195913 A195914 A195915 * A195917 A195918 A195919

Keyword

nonn,easy,tabl

Author

Franklin T. Adams-Watters, Sep 25 2011

Status

approved