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

Author

Omar E. Pol, Dec 07 2009

Keywords

• nonn

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

• 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

Crossrefs

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

Formula

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

Extensions

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