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A152980 First differences of toothpick corner sequence A153006. 50
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, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23, 28, 35, 52, 64, 49, 22, 15, 23, 28, 35, 52, 65, 56, 43, 53, 74, 91, 122, 168, 176, 112, 33, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23, 28, 35, 52 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rows of A152978 when written as a triangle converge to this sequence. - Omar E. Pol, Jul 19 2009

LINKS

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

David Applegate, The movie version

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences

FORMULA

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 below).

EXAMPLE

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

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);

CROSSREFS

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, A153001, A159785, A153004.

Sequence in context: A260167 A035540 A114863 * A170891 A035535 A154309

Adjacent sequences:  A152977 A152978 A152979 * A152981 A152982 A152983

KEYWORD

nonn,look

AUTHOR

Omar E. Pol, Dec 16 2008, Dec 19 2008, Jan 02 2009

EXTENSIONS

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

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

STATUS

approved

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Last modified March 26 10:42 EDT 2017. Contains 284111 sequences.