来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a170876 Showing 1-1 of 1 %I A170876 %S A170876 0,1,5,21,37,53,117,197,261,405,565,789,965,1221,1541,1941,2453,2933, %T A170876 3621,4389,5093,5909,6805,7925,9093,10629,12197,14133,15733,17717, %U A170876 19493,21605,23909,26453,29109,32117,35013,38085,41285 %N A170876 Number of toothpicks after n stages of 3-D toothpick structure defined in Comments. %C A170876 We are in 3-D, and we are placing ordinary toothpicks, as in A139250. %C A170876 We start with one toothpick in the z direction %C A170876 We place toothpicks at any free end, as in A139250. %C A170876 We always place new toothpicks in pairs, two perpendicular toothpicks that are perpendicular to the original toothpick %C A170876 The toothpicks are always in 2 out of the 3 (x, y or z) directions. %C A170876 The initial values are as follows (this should be checked!): %C A170876 n:.0..1..2..3..4..5..6 %C A170876 ---------------------------- %C A170876 x..0..0..2..4..8..4.24 (Number added in x direction) %C A170876 y..0..0..2..4..8..4.24 (Number added in y direction) %C A170876 z..0..1..0..8..0..8.16 (Number added in z direction) %C A170876 ---------------------------- %C A170876 ...0..1..4.16.16.16.64 (Total number added at n-th stage, A170876) %C A170876 ---------------------------- %C A170876 a..0..1..5.21.37.53.117 (Total so far, this sequence) %C A170876 ---------------------------- %H A170876 David Applegate, Omar E. Pol and N. J. A. Sloane,基于细胞自动机的牙签序列及其他序列国会议员,第206卷(2010),157—191页。[定理6中有一个类型:(13)应该读取u(n)=4.3 ^(Wt(n-1)-1),对于n>=2。OEIS中的Toothpick目录和元胞自动机序列%H A170876 R. J. Mathar,C++程序%H A170876 R. J. Mathar,第1阶段后的观点%H A170876 R. J. Mathar,第2阶段后的观点%H A170876 R. J. Mathar,第3阶段后的观点%H A170876 R. J. Mathar,第4阶段后的观点%H A170876 R. J. Mathar,第5阶段后的观点%H A170876 R. J. Mathar,第6阶段后的观点%H A170876 R. J. Mathar,第7阶段后的观点%H A170876 R. J. Mathar,第8阶段后的观点%H A170876 R. J. Mathar,第9阶段后的观点%H A170876 R. J. Mathar,第10阶段后的观点%H A170876 Omar E. Pol,初始条款说明%E A170876在第2阶段,我们有一个水平的十字架,一个垂直的牙签,另一个水平的十字架,总共有5个牙签。%E E 170876,然后我们在十字架的两端加上8个垂直的牙签和8个水平的牙签在十字架的同一平面上,总共有21个牙签。对于另一个版本,见A170837 .A%0876 No.0%8O A170876 0,3‰A170876,N.J.A.SLaNeNez,Jo.05 2010,基于来自R .J.MathARGy的电子邮件,Jun MaTARSY,Jun 08 02,Jun 08 2010,Jun 09 09 2010‰内容修订的Jun 02,2009在OEIS最终用户许可协议下可用: