|
%I #46 Mar 05 2015 13:28:53
%S 1,5,9,21,25,37,53,85,89,101,117,149,165,205,257,341,345,357,373,405,
%T 421,461,513,597,613,653,705,797,857,989,1141,1365,1369,1381,1397,
%U 1429,1445,1485,1537,1621,1637,1677,1729,1821,1881,2013,2165,2389,2405,2445,2497
%N 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 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 The graphs of both A162795 and this sequence are intertwined.
%C 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 a(43) = 1729 is also the Hardy-Ramanujan number.
%H 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 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F a(n) = (A147562(n) + A169707(n))/2.
%F 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 a(43) = (1705 + 1753)/2 = 3458/2 = 1729.
%Y Cf. A001235, A048645, A139250, A147562, A160164, A162795, A169707.
%K nonn,look
%O 1,2
%A _Omar E. Pol_, Feb 21 2015
|
