A101979 Antidiagonal sums of A101309, which is the matrix logarithm of A047999 (Pascal's triangle mod 2).

0, 1, 1, 0, 2, 1, 1, 0, 2, 1, 3, 0, 2, 1, 1, 0, 2, 1, 3, 0, 4, 1, 3, 0, 2, 1, 3, 0, 2, 1, 1, 0, 2, 1, 3, 0, 4, 1, 3, 0, 4, 1, 5, 0, 4, 1, 3, 0, 2, 1, 3, 0, 4, 1, 3, 0, 2, 1, 3, 0, 2, 1, 1, 0, 2, 1, 3, 0, 4, 1, 3, 0, 4, 1, 5, 0, 4, 1, 3, 0, 4, 1, 5, 0, 6, 1, 5, 0, 4, 1, 5, 0, 4, 1, 3, 0, 2, 1, 3, 0, 4, 1, 3, 0, 4

Offset: 0

Author

Paul D. Hanna, Dec 23 2004

Keywords

• nonn

Comments

Partial sums at positions 2^m-1 = m*2^(m-2) for m>=2.

Examples

			Partial sums at 2^m-1 are:
at 2^2-1 (m=2): 0+1+1+0 = 2 = 2*2^(2-2),
at 2^3-1 (m=3): 0+1+1+0+2+1+1+0 = 6 = 3*2^(3-2),
at 2^4-1 (m=4): 0+1+1+0+2+1+1+0+2+1+3+0+2+1+1+0 = 16 = 4*2^(4-2).
		

Crossrefs

Cf. A047999, A101309.

Programs

PARI

{a(n)=sum(k=0,(n-1)\2,if(bitxor(n-k,k)==2^valuation(bitxor(n-k,k),2),1,0))}