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A170893 First differences of the toothpick sequence A170892. 5
0, 1, 1, 2, 4, 4, 4, 8, 10, 10, 4, 8, 10, 12, 12, 22, 26, 18, 4, 8, 10, 12, 12, 22, 26, 20, 12, 22, 28, 32, 42, 66, 66, 34, 4, 8, 10, 12, 12, 22, 26, 20, 12, 22, 28, 32, 42, 66, 66, 36, 12, 22, 28, 32, 42, 66, 68, 48, 42, 68, 84, 102, 146, 194, 162, 66, 4, 8, 10, 12, 12, 22, 26, 20, 12, 22, 28, 32, 42, 66, 66, 36, 12, 22, 28, 32, 42, 66, 68, 48, 42, 68, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

This describes how many toothpicks are added at each step (as to form the upper bar of a T) at all "exposed" endpoints, starting from an initial configuration with a vertical toothpick whose lower endpoint rests on the top of the conic region { (x,y): y < -|x| } into which the toothpicks may not extend. - M. F. Hasler, Jan 30 2013

LINKS

Table of n, a(n) for n=0..92.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

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

EXAMPLE

From Omar E. Pol, Jan 30 2013 (Start):

If written as an irregular triangle in which rows 0..2 have length 1, it appears that row j has length 2^(j-3), if j >= 3.

0;

1;

1;

2;

4,4;

4,8,10,10;

4,8,10,12,12,22,26,18;

4,8,10,12,12,22,26,20,12,22,28,32,42,66,66,34;

4,8,10,12,12,22,26,20,12,22,28,32,42,66,66,36,12,22,28,32,42,66,68,48,42,68,84,102,146,194,162,66;

4,8,10,12,12,22,26,20,12,22,28,32,42,66,66,36,12,22,28,32,42,66,68,48,42,68,84,...

(End)

PROG

(PARI) A170893(n, print_all=0)={my( ee=[[2*I, I]], p=Set( concat( vector( 2*n-(n>0), k, k-n-abs(k-n)*I ), I ))); print_all & print1("1, 1"); for(i=3, n, p=setunion(p, Set(Mat(ee~)[, 1])); my(c, d, ne=[]); for( k=1, #ee, setsearch(p, c=ee[k][1]+d=ee[k][2]*I) || ne=setunion(ne, Set([[c, d]])); setsearch(p, c-2*d) || ne=setunion(ne, Set([[c-2*d, -d]]))); forstep( k=#ee=eval(ne), 2, -1, ee[k][1]==ee[k-1][1] & k-- & ee=vecextract(ee, Str("^"k"..", k+1))); print_all & print1(", "#ee)); (n>0)*#ee} \\ M. F. Hasler, Jan 30 2013

CROSSREFS

Cf. A139250, A139251, A160407, A170887, A170889, A170891, A170892.

Sequence in context: A076345 A327331 A231349 * A194445 A220525 A160809

Adjacent sequences: A170890 A170891 A170892 * A170894 A170895 A170896

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jan 09 2010

EXTENSIONS

Values beyond a(10) from M. F. Hasler, Jan 30 2013

STATUS

approved

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Last modified December 5 12:42 EST 2022. Contains 358586 sequences. (Running on oeis4.)