0,1

a(n) = sum_{i >= 0} binomial(A000120(n+i),i)

For k >= 1, a(2^k-2) = k+1 and a(2^k-1) = 3; otherwise if n = 2^i + j, 0 <= j <= 2^i-3, a(n) = a(j) + a(j+1).

a(n) = 2*A151552(n) + A151552(n-1).

a(5) = binomial(2,0) + binomial(2,1) + binomial(3,2) + binomial(1,3) + binomial(2,4) + binomial(2,5) + ... = 1 + 2 + 3 + 0 + 0 + 0 + ... = 6

Contribution from Omar E. Pol (info(AT)polprimos.com), Jun 09 2009: (Start)

Triangle begins:

2;

3;3;

3,5,6,4;

3,5,6,6,8,11,10,5;

3,5,6,6,8,11,10,7,8,11,12,14,19,21,15,6;

3,5,6,6,8,11,10,7,8,11,12,14,19,21,15,8,8,11,12,14,19,21,17,15,19,23,26,...

(End)

See A118977 for Maple code.

For generating functions of the form Prod_{k>=c} (1+a*x^(2^k-1)+b*x^2^k)) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694

Row sums of A151683. See A151687 for another version.

Cf. A151552 (G.f. has one factor fewer)

Limiting form of rows of A118977 when that sequence is written as a triangle and the initial 1 is omitted. - N. J. A. Sloane, Jun 01 2009.

Cf. A000079. [From Omar E. Pol (info(AT)polprimos.com), Jun 09 2009]

Sequence in context: A014202 A145281 A151687 this_sequence A141418 A130499 A020910

Adjacent sequences: A160570 A160571 A160572 this_sequence A160574 A160575 A160576

nonn

Hagen von Eitzen (math(AT)redeker.de), May 20 2009