%N Length of the n-th edge of an L-toothpick structure which gives Recaman's sequence A005132.
%C Consider a toothpick structure formed by L-toothpicks connected by their endpoints. The endpoints of the L-toothpics are placed on the main diagonal of the first quadrant. At stage 1 we place an L-toothpick with one of its endpoints on the origin. At stage n we place an L-toothpick of size n. The L-toothpicks are placed alternately, on one or another sector of the first quadrant, trying to make the structure has an exposed endpoint closest to the origin. The total length of all L-toothpicks after n-th stage is A002378(n). The value of x and y of the endpoint of the structure after n-th stage is equal to the n-th term of Recaman's sequence A005132(n). Note that we can get other illustrations of initial terms for Recaman's sequence by replacing each L-toothpick by an Q-toothpick or also by a semicircumference. This structure is also one of the three views of the three-dimensional model for the Recaman's sequence. For more information about L-toothpicks and Q-toothpicks see A172310 and A187210.
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/toothlist.html">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recaman'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 L-toothpicks:
%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, A210608-A210613.
%A _Omar E. Pol_, Mar 24 2012