%I
%S 1,3,5,3,4,4,5,11,13,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,
%T 16,17,17
%N Length of the nth edge of an Ltoothpick structure which gives Recamán's sequence A005132.
%C Consider a toothpick structure formed by Ltoothpicks connected by their endpoints. The endpoints of the Ltoothpicks are placed on the main diagonal of the first quadrant. At stage 1 we place an Ltoothpick with one of its endpoints on the origin. At stage n we place an Ltoothpick of size n. The Ltoothpicks are placed alternately, on one or another sector of the first quadrant, trying to make the structure have an exposed endpoint closest to the origin. The total length of all Ltoothpicks after the nth stage is A002378(n). The value of x and y of the endpoint of the structure after the nth stage is equal to the nth term of Recamán's sequence A005132(n). Note that we can get other illustrations of initial terms of Recamán's sequence by replacing each Ltoothpick by a Qtoothpick or by a semicircumference. This structure is also one of the three views of the threedimensional model for Recamán's sequence. For more information about Ltoothpicks and Qtoothpicks, see A172310 and A187210.
%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>
%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>
%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%e The summands are the size of the Ltoothpicks:
%e a(1) = 1.
%e a(2) = 1 + 2 = 3.
%e a(3) = 2 + 3 = 5.
%e a(4) = 3.
%e a(5) = 4.
%e a(6) = 4.
%e a(7) = 5.
%e a(8) = 5 + 6 = 11.
%e a(9) = 6 + 7 = 13.
%e a(10) = 7.
%Y First differences of A210607.
%Y Cf. A005132, A064289, A119632, A139250, A160356, A160357, A171175, A171178, A172310, A187210, A210604, A210605, A210608A210613.
%K nonn,more
%O 1,2
%A _Omar E. Pol_, Mar 24 2012
