A168112 Toothpick sequence starting with a straight line, with angle = Pi/4, from which protrudes a half toothpick.

0, 1, 2, 4, 7, 10, 13, 19, 26, 32, 35, 41, 48, 56, 65, 81, 98, 108, 111, 117, 124, 132, 141, 157, 174, 186, 195, 211, 230, 252, 283, 329, 370, 388, 391, 397, 404, 412, 421, 437, 454, 466, 475, 491, 510, 532, 563, 609, 650, 670

Offset

0,3

Comments

On the infinite square grid, we start at round 0 drawing a straight line, with angle = Pi/4, from which protrudes a half toothpick.

At round 1 we place an orthogonal toothpick centered at the end.

In each subsequent round, for every exposed toothpick end, place an orthogonal toothpick centered at that end.

The sequence gives the number of toothpicks after n rounds.

See also A168113, the first differences.

For more information see A139250, which is the main entry for this sequence.

Links

Table of n, a(n) for n=0..49.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

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

Formula

a(n) = A160730(n)/2. [From Nathaniel Johnston, Mar 28 2011]

Crossrefs

Cf. A139250, A139251, A153000, A153006, A160406, A168113, A168114.

Sequence in context: A194172 A173537 A049983 * A170894 A151986 A287522

Adjacent sequences: A168109 A168110 A168111 * A168113 A168114 A168115

Keyword

nonn

Author

Omar E. Pol, Dec 07 2009

Extensions

Terms after a(34) from Nathaniel Johnston, Mar 28 2011

Status

approved