cp's OEIS Frontend

A255366 Total number of ON cells at stage n of two-dimensional cellular automaton defined by the rules of the "Ulam-Warburton" two-dimensional cellular automaton (A147562) for two of its wedges and defined by "Rule 750" using the von Neumann neighborhood (A169707) for the two other wedges.

%I A255366 #46 Mar 05 2015 13:28:53
%S A255366 1,5,9,21,25,37,53,85,89,101,117,149,165,205,257,341,345,357,373,405,
%T A255366 421,461,513,597,613,653,705,797,857,989,1141,1365,1369,1381,1397,
%U A255366 1429,1445,1485,1537,1621,1637,1677,1729,1821,1881,2013,2165,2389,2405,2445,2497
%N A255366 Total number of ON cells at stage n of two-dimensional cellular automaton defined by the rules of the "Ulam-Warburton" two-dimensional cellular automaton (A147562) for two of its wedges and defined by "Rule 750" using the von Neumann neighborhood (A169707) for the two other wedges.
%C A255366 First differs from A162795 at a(14), but it appears that then they share infinitely many terms. It appears that this is very close to A162795 rather than both A147562 and A169707.
%C A255366 The graphs of both A162795 and this sequence are intertwined.
%C A255366 Note that there are four main versions of this cellular automaton, depending on whether the wedges with the same rule are opposite or perpendicular and also depending on whether each mentioned version is represented by the "one-step rook" illustration or by the "one-step bishop" illustration. The four versions are represented by this sequence.
%C A255366 a(43) = 1729 is also the Hardy-Ramanujan number.
%H A255366 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 A255366 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A255366 a(n) = (A147562(n) + A169707(n))/2.
%F A255366 It appears that a(n) = A147562(n) = A162795(n) = A169709(n), if n is a member of A048645, or in other words: if the binary weight of n is 1 or 2, but note that a(n) = A162795(n) for many other values of n.
%e A255366 a(43) = (1705 + 1753)/2 = 3458/2 = 1729.
%Y A255366 Cf. A001235, A048645, A139250, A147562, A160164, A162795, A169707.
%K A255366 nonn,look
%O A255366 1,2
%A A255366 _Omar E. Pol_, Feb 21 2015