cp's OEIS Frontend

A288775 Difference between the total number of toothpicks in the toothpick structure of A139250 that are parallel to the initial toothpick after n odd stages, and the total number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton of A147562.

%I A288775 #32 Jul 07 2017 08:11:48
%S A288775 0,0,0,0,0,0,4,0,0,0,4,0,4,4,28,0,0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,
%T A288775 0,0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0,4,4,28,4,28,32,132,4,28,32,
%U A288775 132,32,136,176,524,0,0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0,4,4,28,4,28,32,132,4,28,32
%N A288775 Difference between the total number of toothpicks in the toothpick structure of A139250 that are parallel to the initial toothpick after n odd stages, and the total number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton of A147562.
%C A288775 It appears that a(n) = 0 if and only if n is a member of A048645.
%C A288775 First differs from A255263 at a(14), with which it shares infinitely many terms.
%C A288775 It appears that A147562(n) = A162795(n) = A169707(n) = A255366(n) = A256250(n) = A256260(n), if n is a member of A048645.
%H A288775 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 A288775 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A288775 a(n) = A162795(n) - A147562(n).
%e A288775 Written as an irregular triangle T(j,k), k>=1, in which the row lengths are the terms of A011782, the sequence begins:
%e A288775 0;
%e A288775 0;
%e A288775 0,0;
%e A288775 0,0,4,0;
%e A288775 0,0,4,0,4,4,28,0;
%e A288775 0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0;
%e A288775 0,0,4,0,4,4,28,0,4,4,28,4,28,32,132,0,4,4,28,4,28,32,132,4,28,32,132,32,136,176,524,0;
%e A288775 ...
%e A288775 It appears that if k is a power of 2 then T(j,k) = 0.
%e A288775 It appears that every column lists the same terms as its initial term.
%Y A288775 Cf. A011782, A048645, A139250, A139251, A147562, A147582, A162793, A162795, A169707, A255263, A255366, A256250, A256260.
%K A288775 nonn,tabf
%O A288775 1,7
%A A288775 _Omar E. Pol_, Jul 04 2017