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%I #56 Feb 14 2017 15:17:01
%S 0,1,1,3,1,3,5,7,1,3,5,7,5,11,17,15,1,3,5,7,5,11,17,15,5,11,17,23,29,
%T 35,41,31,1,3,5,7,5,11,17,15,5,11,17,23,29,35,41,31,5,11,17,23,29,35,
%U 41,47,53,59,65,71,77,83,89,63,1,3,5,7,5,11,17,15,5,11,17,23,29,35,41,31,5,11,17,23,29,35,41,47,53,59,65,71,77,83,89
%N Triangle read by rows: T(j,k) = 2*k-1 if k is a power of 2, otherwise, between positions that are powers of 2 we have the initial terms of A016969, with j>=0, 1<=k<=A011782(j) and T(0,1) = 0.
%C Partial sums give A256264.
%C First differs from A160552 at a(27).
%C Appears to be a canonical sequence partially related to the cellular automata of A139250, A147562, A162795, A169707, A255366, A256250. See also A256264 and A256260.
%H Ivan Neretin, <a href="/A256263/b256263.txt">Table of n, a(n) for n = 0..8191</a>
%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>
%e Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
%e 0;
%e 1;
%e 1,3;
%e 1,3,5,7;
%e 1,3,5,7,5,11,17,15;
%e 1,3,5,7,5,11,17,15,5,11,17,23,29,35,41,31;
%e 1,3,5,7,5,11,17,15,5,11,17,23,29,35,41,31,5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,63;
%e ...
%e Right border gives A000225.
%e Apart from the initial 0 the row sums give A000302.
%e Rows converge to A256258.
%e .
%e Illustration of initial terms in the fourth quadrant of the square grid:
%e ---------------------------------------------------------------------------
%e n a(n) Compact diagram
%e ---------------------------------------------------------------------------
%e 0 0 _
%e 1 1 |_|_ _
%e 2 1 |_| |
%e 3 3 |_ _|_ _ _ _
%e 4 1 |_| | | |
%e 5 3 |_ _| | |
%e 6 5 |_ _ _| |
%e 7 7 |_ _ _ _|_ _ _ _ _ _ _ _
%e 8 1 |_| | | |_ _ | |
%e 9 3 |_ _| | |_ | | |
%e 10 5 |_ _ _| | | | | |
%e 11 7 |_ _ _ _| | | | |
%e 12 5 | | |_ _ _| | | |
%e 13 11 | |_ _ _ _ _| | |
%e 14 17 |_ _ _ _ _ _ _| |
%e 15 15 |_ _ _ _ _ _ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e 16 1 |_| | | |_ _ | |_ _ _ _ _ _ | |
%e 17 3 |_ _| | |_ | | |_ _ _ _ _ | | |
%e 18 5 |_ _ _| | | | | |_ _ _ _ | | | |
%e 19 7 |_ _ _ _| | | | |_ _ _ | | | | |
%e 20 5 | | |_ _ _| | | |_ _ | | | | | |
%e 21 11 | |_ _ _ _ _| | |_ | | | | | | |
%e 22 17 |_ _ _ _ _ _ _| | | | | | | | | |
%e 23 15 |_ _ _ _ _ _ _ _| | | | | | | | |
%e 24 5 | | | | | | |_ _ _| | | | | | | |
%e 25 11 | | | | | |_ _ _ _ _| | | | | | |
%e 26 17 | | | | |_ _ _ _ _ _ _| | | | | |
%e 27 23 | | | |_ _ _ _ _ _ _ _ _| | | | |
%e 28 29 | | |_ _ _ _ _ _ _ _ _ _ _| | | |
%e 29 35 | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e 30 41 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
%e 31 31 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e .
%e a(n) is also the number of cells in the n-th region of the diagram.
%e A256264(n) gives the total number of cells after n-th stage.
%t Flatten@Join[{0}, NestList[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 6]] (* _Ivan Neretin_, Feb 14 2017 *)
%Y Cf. A000225, A000302, A011782, A038573, A006257, A016969, A139251, A160552, A256250, A256258, A256260, A256261, A256264, A256265.
%K nonn,tabf,look
%O 0,4
%A _Omar E. Pol_, Mar 30 2015
%E Terms a(95) to a(98) fixed by _Ivan Neretin_, Feb 14 2017
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