A170892 Toothpick sequence similar to A160406, but always staying outside the wedge, starting at stage 1 with a vertical toothpick whose endpoint touches the vertex of the wedge.

0, 1, 2, 4, 8, 12, 16, 24, 34, 44, 48, 56, 66, 78, 90, 112, 138, 156, 160, 168, 178, 190, 202, 224, 250, 270, 282, 304, 332, 364, 406, 472, 538, 572, 576, 584, 594, 606, 618, 640, 666, 686, 698, 720, 748, 780, 822, 888, 954, 990, 1002, 1024, 1052, 1084, 1126, 1192, 1260, 1308, 1350, 1418, 1502, 1604, 1750, 1944

Offset: 0

Author

Omar E. Pol, Jan 09 2010

Keywords

• nonn

Comments

See A170893 for the first differences.

Links

• 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

Crossrefs

Cf. A139250, A160406, A170886, A170888, A170890, A170893.

Programs

PARI

A170892(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 )), cnt=2); print_all & print1("1,2"); n<3 & return(n); 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))); cnt+=#ee; print_all & print1(","cnt)); cnt} \\ - M. F. Hasler, Jan 30 2013

Extensions

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