0,2

Rows of A152978 when written as a triangle converge to this sequence. [From Omar E. Pol (info(AT)polprimos.com), Jul 19 2009]

N. J. A. Sloane, Table of n, a(n) for n = 0..16384

Index entries for sequences related to toothpick sequences

G.f.: (1 + x) * Prod_{ n >= 1} (1 + x^(2^n-1) + 2*x^(2^n)). - N. J. A. Sloane, May 20, 2009, corrected May 21 2009

For formula see A147646 (or, better, see the Maple code here).

Triangle begins:

.1;

.2;

.3,3;

.4,7,8,5;

.4,7,9,10,15,22,20,9;

.4,7,9,10,15,22,21,14,15,23,28,35,52,64,48,17;

....

Rows converge to A153001. - N. J. A. Sloane, Jun 07 2009

Maple code from N. J. A. Sloane, May 18 2009. First define old version with offset 1:

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

if n <= 0 then RETURN(0); fi;

if n <= 2 then RETURN(2^(n-1)); fi;

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

j:=n-2^i;

if j=0 then RETURN(n/2+1); fi;

if j<2^i-1 then RETURN(2*S(j)+S(j+1)); fi;

if j=2^i-1 then RETURN(2*S(j)+S(j+1)-1); fi;

-1;

end;

# Now change the offset:

T:=n->S(n+1);

G := (1 + x) * mul(1 + x^(2^k-1) + 2*x^(2^k), k=1..20); - N. J. A. Sloane, May 20, 2009, corrected May 21 2009

Equals A151688 divided by 2. - N. J. A. Sloane, Jun 03 2009

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

Equals A147646/4. - N. J. A. Sloane, May 01 2009

Cf. A139250, A139251, A152968, A152978, A153006.

Cf. A153001, A159785. [From Omar E. Pol (info(AT)polprimos.com), Jun 07 2009]

CF. A153004. [From Omar E. Pol (info(AT)polprimos.com), Jul 19 2009]

Sequence in context: A119614 A035540 A114863 this_sequence A035535 A154309 A140514

Adjacent sequences: A152977 A152978 A152979 this_sequence A152981 A152982 A152983

nonn

Omar E. Pol (info(AT)polprimos.com), Dec 16 2008, Dec 19 2008, Jan 02 2009

More terms (based on A147646) from N. J. A. Sloane, May 01 2009

Offset changed by N. J. A. Sloane, May 18 2009