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%I #24 Feb 24 2021 02:48:19
%S 0,1,2,4,8,12,16,24,34,44,48,56,66,78,90,112,138,156,160,168,178,190,
%T 202,224,250,270,282,304,332,364,406,472,538,572,576,584,594,606,618,
%U 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
%N 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.
%C See A170893 for the first differences.
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%o (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
%Y Cf. A139250, A160406, A170886, A170888, A170890, A170893.
%K nonn
%O 0,3
%A _Omar E. Pol_, Jan 09 2010
%E Terms beyond a(10) from _M. F. Hasler_, Jan 30 2013
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