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 A187214 Number of gulls (or G-toothpicks) added at n-th stage in the first quadrant of the gullwing structure of A187212. 0
 0, 1, 1, 2, 2, 4, 5, 4, 2, 4, 6, 6, 8, 14, 15, 8, 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 39, 16, 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 40, 18, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 95 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS It appears that both a(2) and a(2^k - 1) are odd numbers, for k >= 2. Other terms are even numbers. 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 FORMULA a(1)=0. a(n) = A187213(n)/2, for n >= 2. It appears that a(2^k - 1) = A099035(k-1), for k >= 2. EXAMPLE At stage 1 we start in the first quadrant from a Q-toothpick centered at (1,0) with its endpoints at (0,0) and (1,1). There are no gulls in the structure, so a(1) = 0. At stage 2 we place a gull (or G-toothpick) with its midpoint at (1,1) and its endpoints at (2,0) and (2,2), so a(2) = 1. There is only one exposed midpoint at (2,2). At stage 3 we place a gull with its midpoint at (2,2), so a(3) = 1. There are two exposed endpoints. At stage 4 we place two gulls, so a(4) = 2. There are two exposed endpoints. At stage 5 we place two gulls, so a(5) = 2. There are four exposed endpoints. And so on. If written as a triangle begins: 0, 1, 1,2, 2,4,5,4, 2,4,6,6,8,14,15,8, 2,4,6,6,8,14,16,10,8,14,18,20,30,44,39,16, 2,4,6,6,8,14,16,10,8,14,18,20,30,44,40,18,8,14,18,20,30,44,42,28,... It appears that rows converge to A151688. MAPLE read("transforms3") ; L := BFILETOLIST("b187212.txt") ; A187213 := DIFF(L) ; seq( op(n, A187213)/2, n=2..nops(A187213)) ; # R. J. Mathar, Mar 30 2011 CROSSREFS Cf. A099035, A151550, A151688, A187210, A187211, A187212, A187213, A187220. Sequence in context: A186053 A133082 A130265 * A179821 A292272 A292248 Adjacent sequences:  A187211 A187212 A187213 * A187215 A187216 A187217 KEYWORD nonn AUTHOR Omar E. Pol, Mar 22 2011, Apr 06 2011 STATUS approved

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Last modified May 12 09:16 EDT 2021. Contains 343821 sequences. (Running on oeis4.)