A187214 Number of gulls (or G-toothpicks) added at n-th stage in the first quadrant of the gullwing structure of A187212.
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
Offset: 1
Keywords
Examples
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.
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
Programs
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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
Comments