A160420 Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose skeleton is the same network as the toothpick structure of A139250 but with toothpicks of length 4.
0, 5, 13, 27, 41, 57, 85, 123, 149, 165, 193, 233, 277, 337, 429, 527, 577, 593, 621, 661, 705, 765, 857, 957, 1025, 1085, 1181, 1305, 1453, 1665, 1945, 2187, 2285, 2301, 2329, 2369, 2413, 2473, 2565, 2665, 2733, 2793, 2889, 3013, 3161, 3373, 3653, 3897, 4013
Offset: 0
Keywords
Examples
a(2)=13: .o-o-o-o-o .....|.... .....o.... .....|.... .....o.... .....|.... .....o.... .....|.... .o-o-o-o-o
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
Formula
The above conjecture is true: each toothpick covers exactly two more grid points than the corresponding toothpick in A147614.
Extensions
Definition revised by N. J. A. Sloane, Jan 02 2010.
Formula verified and more terms from Nathaniel Johnston, Nov 13 2010
Comments