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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

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: A076340 A076345 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 February 21 21:41 EST 2018. Contains 299427 sequences. (Running on oeis4.)