A168112 - OEIS

%I #12 Feb 24 2021 02:48:18

%S 0,1,2,4,7,10,13,19,26,32,35,41,48,56,65,81,98,108,111,117,124,132,

%T 141,157,174,186,195,211,230,252,283,329,370,388,391,397,404,412,421,

%U 437,454,466,475,491,510,532,563,609,650,670

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

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

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

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

%C The sequence gives the number of toothpicks after n rounds.

%C See also A168113, the first differences.

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

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]

%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>

%F a(n) = A160730(n)/2. [From _Nathaniel Johnston_, Mar 28 2011]

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

%K nonn

%O 0,3

%A _Omar E. Pol_, Dec 07 2009

%E Terms after a(34) from _Nathaniel Johnston_, Mar 28 2011