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A210606 Length of the n-th edge of an L-toothpick structure which gives Recamán's sequence A005132. 11
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, 16, 17, 17 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..30.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to Recamán's sequence

Index entries for sequences related to toothpick sequences


The summands are the size of the L-toothpicks:

a(1) = 1.

a(2) = 1 + 2 = 3.

a(3) = 2 + 3 = 5.

a(4) = 3.

a(5) = 4.

a(6) = 4.

a(7) = 5.

a(8) = 5 + 6 = 11.

a(9) = 6 + 7 = 13.

a(10) = 7.


First differences of A210607.

Cf. A005132, A064289, A119632, A139250, A160356, A160357, A171175, A171178, A172310, A187210, A210604, A210605, A210608-A210613.

Sequence in context: A077934 A077950 A077973 * A254327 A175999 A236965

Adjacent sequences:  A210603 A210604 A210605 * A210607 A210608 A210609




Omar E. Pol, Mar 24 2012



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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)