

A210606


Length of the nth edge of an Ltoothpick 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
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OFFSET

1,2


COMMENTS

Consider a toothpick structure formed by Ltoothpicks connected by their endpoints. The endpoints of the Ltoothpics 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.


LINKS

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


EXAMPLE

The summands are the size of the Ltoothpicks:
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.


CROSSREFS

First differences of A210607.
Cf. A005132, A064289, A119632, A139250, A160356, A160357, A171175, A171178, A172310, A187210, A210604, A210605, A210608A210613.
Sequence in context: A077934 A077950 A077973 * A254327 A175999 A236965
Adjacent sequences: A210603 A210604 A210605 * A210607 A210608 A210609


KEYWORD

nonn,more


AUTHOR

Omar E. Pol, Mar 24 2012


STATUS

approved



