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

0,5

Comments

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

Links

Table of n, a(n) for n=0..104.

Example

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).

Prog

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

Crossrefs

Cf. A047999, A101309.

Sequence in context: A230121 A029375 A071462 * A369241 A308061 A339448

Adjacent sequences: A101976 A101977 A101978 * A101980 A101981 A101982

Keyword

nonn

Author

Paul D. Hanna, Dec 23 2004

Status

approved