

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
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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^(j3), 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, knabs(kn)*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, c2*d)  ne=setunion(ne, Set([[c2*d, d]]))); forstep( k=#ee=eval(ne), 2, 1, ee[k][1]==ee[k1][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



