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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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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.]
PROG
(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
CROSSREFS
Sequence in context: A317804 A328524 A322447 * A246468 A360641 A326807
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 09 2010
EXTENSIONS
Terms beyond a(10) from M. F. Hasler, Jan 30 2013
STATUS
approved

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Last modified April 23 15:20 EDT 2024. Contains 371916 sequences. (Running on oeis4.)