cp's OEIS Frontend

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

%I A255264 #38 Dec 17 2021 20:34:55
%S A255264 1,5,9,21,25,37,85,89,101,149,341,345,357,405,597,1365,1369,1381,1429,
%T A255264 1621,2389,5461,5465,5477,5525,5717,6485,9557,21845,21849,21861,21909,
%U A255264 22101,22869,25941,38229,87381,87385,87397,87445,87637
%N A255264 Total number of ON cells in the "Ulam-Warburton" two-dimensional cellular automaton of A147562 after A048645(n) generations.
%C A255264 It appears that these are the terms of A147562, A162795, A169707, A255366, A256250, A256260, whose indices have binary weight 1 or 2.
%H A255264 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>
%H A255264 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A255264 a(n) = A147562(A048645(n)).
%F A255264 Conjecture 1: a(n) = A162795(A048645(n)).
%F A255264 Conjecture 2: a(n) = A169707(A048645(n)).
%F A255264 Conjecture 3: a(n) = A255366(A048645(n)).
%F A255264 Conjecture 4: a(n) = A256250(A048645(n)).
%F A255264 Conjecture 5: a(n) = A256260(A048645(n)).
%F A255264 a(n) = A032925(A209492(n-1)) (conjectured). - _Jon Maiga_, Dec 17 2021
%e A255264 Also, written as an irregular triangle in which row lengths are the terms of A028310 the sequence begins:
%e A255264       1;
%e A255264       5;
%e A255264       9,    21;
%e A255264      25,    37,    85;
%e A255264      89,   101,   149,   341;
%e A255264     345,   357,   405,   597,  1365;
%e A255264    1369,  1381,  1429,  1621,  2389,  5461;
%e A255264    5465,  5477,  5525,  5717,  6485,  9557, 21845;
%e A255264   21849, 21861, 21909, 22101, 22869, 25941, 38229, 87381;
%e A255264   ...
%e A255264 Right border gives the positive terms of A002450.
%e A255264 It appears that the second leading diagonal gives the odd terms of A206374.
%Y A255264 Cf. A002450, A028310, A032925, A048645, A075897, A139250, A147562, A162795, A169707, A206374, A209492, A255263, A255366, A256250, A256260.
%K A255264 nonn,tabf,look
%O A255264 1,2
%A A255264 _Omar E. Pol_, Feb 19 2015