|
%I #65 Oct 31 2017 21:28:59
%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 n-th edge of an L-toothpick structure which gives Recamán's sequence A005132.
%C Consider a toothpick structure formed by L-toothpicks connected by their endpoints. The endpoints of the L-toothpicks 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 have an exposed endpoint closest to the origin. The total length of all L-toothpicks after the n-th stage is A002378(n). The value of x and y of the endpoint of the structure after the n-th stage is equal to the n-th term of Recamán's sequence A005132(n). Note that we can get other illustrations of initial terms of Recamán's sequence by replacing each L-toothpick by a Q-toothpick or by a semicircumference. This structure is also one of the three views of the three-dimensional model for Recamán's sequence. For more information about L-toothpicks and Q-toothpicks, 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 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.
%K nonn,more
%O 1,2
%A _Omar E. Pol_, Mar 24 2012
|
