A256537
First differences of corner sequence A256536 associated with A151723.
Original entry on oeis.org
1, 3, 5, 9, 9, 9, 17, 25, 17, 9, 17, 29, 37, 33, 41, 57, 33, 9, 17, 29, 37, 37, 53, 85, 85, 49, 41, 73, 101, 93, 101, 125, 65, 9, 17, 29, 37, 37, 53, 85, 85, 53, 53, 93, 133, 141, 149, 197, 181, 81, 41, 73, 101, 109, 141, 221, 253, 173, 117, 173, 249, 237, 237, 265, 129
Offset: 1
Written as an irregular triangle in which the row lengths are the absolute values of the terms of A141531, the sequence begins:
1;
3;
5;
9, 9;
9, 17, 25, 17;
9, 17, 29, 37, 33, 41, 57, 33;
9, 17, 29, 37, 37, 53, 85, 85, 49, 41, 73, 101, 93, 101, 125, 65;
9, 17, 29, 37, 37, 53, 85, 85, 53, 53, 93, 133, 141, 149, 197, 181, 81, 41, 73, 101, 109, 141, 221, 253, 173, 117, 173, 249, 237, 237, 265, 129;
...
It appears that the right border gives A083318, whose representation in base 2 gives A000533.
A151723
Total number of ON states after n generations of cellular automaton based on hexagons.
Original entry on oeis.org
0, 1, 7, 13, 31, 37, 55, 85, 127, 133, 151, 181, 235, 289, 331, 409, 499, 505, 523, 553, 607, 661, 715, 817, 967, 1069, 1111, 1189, 1327, 1489, 1603, 1789, 1975, 1981, 1999, 2029, 2083, 2137, 2191, 2293, 2443, 2545, 2599, 2701, 2875, 3097, 3295
Offset: 0
- S. M. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215-224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962 (see Example 6, page 224).
- N. J. A. Sloane, Table of n, a(n) for n = 0..4095 [First 1026 terms from David Applegate and N. J. A. Sloane]
- David Applegate, The movie version
- David Applegate and N. J. A. Sloane, Table of n, A151724(n), A151723(n) for n = 0..1025
- 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.]
- Bradley Klee, Log-periodic coloring, over the half-hexagon tiling.
- N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
- N. J. A. Sloane, Exciting Number Sequences (video of talk), Mar 05 2021
Cf.
A147562,
A151724,
A151725,
A161206,
A161644,
A169779,
A169780,
A170898,
A170905,
A182632,
A182840,
A256536,
A256537.
-
A151723[0] = 0; A151723[n_] := Total[CellularAutomaton[{10926, {2, {{2, 2, 0}, {2, 1, 2}, {0, 2, 2}}}, {1, 1}}, {{{1}}, 0}, {{{n - 1}}}], 2]; Array[A151723, 47, 0](* JungHwan Min, Sep 01 2016 *)
A151723L[n_] := Prepend[Total[#, 2] & /@ CellularAutomaton[{10926, {2, {{2, 2, 0}, {2, 1, 2}, {0, 2, 2}}}, {1, 1}}, {{{1}}, 0}, n - 1], 0]; A151723L[46] (* JungHwan Min, Sep 01 2016 *)
Showing 1-2 of 2 results.
Comments