0,2

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009: When convolved with A151575: (1, 0, 2, -2, 6, -10, 22, -42, 86, -170, 342,...) equals the toothpick sequence A139250: (1, 3, 7, 11, 15, 23, 35, 43,...).

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 04 2009: (Start)

Equals A160552: [1, 1, 3, 1, 3, 5,...] convolved with [1, 2, 0, 0, 0,...],

equivalent to a(n) = 2*A160552(n) + A160552(n+1). (End)

a(2^k-1) = 2^(k+1)-1 for k >= 0; otherwise a(2^k) = 5 for k >= 1; otherwise a(2^i+j) = 2a(j)+a(j+1) for i >= 2, 1 <= j <= 2^i-2. - N. J. A. Sloane, May 22 2009

G.f.: 1/(1+x) + 4*x*mul(1+x^(2^k-1)+2*x^(2^k),k=1..oo). - N. J. A. Sloane, May 23 2009

Contribution from Omar E. Pol (info(AT)polprimos.com), Jul 24 2009: (Start)

If written as a triangle:

1;

3;

5,7;

5,11,17,15;

5,11,17,19,21,39,49,31;

5,11,17,19,21,39,49,35,21,39,53,59,81,127,129,63;

5,11,17,19,21,39,49,35,21,39,53,59,81,127,129,67,21,39,53,59,81,127,133,91,...

(End)

G := 1/(1+x) + 4*x*mul(1+x^(2^k-1)+2*x^(2^k), k=1..20); - N. J. A. Sloane, May 23 2009

S2:=proc(n) option remember; local i, j;

if n <= 1 then RETURN(2*n+1); fi;

i:=floor(log(n)/log(2));

j:=n-2^i;

if j=0 then 5 elif j=2^i-1 then 2*n+1

else 2*S2(j)+S2(j+1); fi;

end; # - N. J. A. Sloane, May 22 2009

Cf. A139250, A160552, A151549.

A078008 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2009]

Sequence in context: A141261 A077129 A073409 this_sequence A071581 A084393 A100005

Adjacent sequences: A151545 A151546 A151547 this_sequence A151549 A151550 A151551

nonn

David Applegate (david(AT)research.att.com), May 18 2009