A255264 Total number of ON cells in the "Ulam-Warburton" two-dimensional cellular automaton of A147562 after A048645(n) generations.

1, 5, 9, 21, 25, 37, 85, 89, 101, 149, 341, 345, 357, 405, 597, 1365, 1369, 1381, 1429, 1621, 2389, 5461, 5465, 5477, 5525, 5717, 6485, 9557, 21845, 21849, 21861, 21909, 22101, 22869, 25941, 38229, 87381, 87385, 87397, 87445, 87637

Offset: 1

Author

Omar E. Pol, Feb 19 2015

Keywords

• nonn
• tabf
• look

Comments

It appears that these are the terms of A147562, A162795, A169707, A255366, A256250, A256260, whose indices have binary weight 1 or 2.

Examples

			Also, written as an irregular triangle in which row lengths are the terms of A028310 the sequence begins:
      1;
      5;
      9,    21;
     25,    37,    85;
     89,   101,   149,   341;
    345,   357,   405,   597,  1365;
   1369,  1381,  1429,  1621,  2389,  5461;
   5465,  5477,  5525,  5717,  6485,  9557, 21845;
  21849, 21861, 21909, 22101, 22869, 25941, 38229, 87381;
  ...
Right border gives the positive terms of A002450.
It appears that the second leading diagonal gives the odd terms of A206374.
		

Links

• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A002450, A028310, A032925, A048645, A075897, A139250, A147562, A162795, A169707, A206374, A209492, A255263, A255366, A256250, A256260.

Formula

a(n) = A147562(A048645(n)).

Conjecture 1: a(n) = A162795(A048645(n)).

Conjecture 2: a(n) = A169707(A048645(n)).

Conjecture 3: a(n) = A255366(A048645(n)).

Conjecture 4: a(n) = A256250(A048645(n)).

Conjecture 5: a(n) = A256260(A048645(n)).

a(n) = A032925(A209492(n-1)) (conjectured). - Jon Maiga, Dec 17 2021