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A256263 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.

%I A256263 #56 Feb 14 2017 15:17:01
%S A256263 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 A256263 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 A256263 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 A256263 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 A256263 Partial sums give A256264.
%C A256263 First differs from A160552 at a(27).
%C A256263 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 A256263 Ivan Neretin, <a href="/A256263/b256263.txt">Table of n, a(n) for n = 0..8191</a>
%H A256263 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 A256263 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A256263 Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
%e A256263 0;
%e A256263 1;
%e A256263 1,3;
%e A256263 1,3,5,7;
%e A256263 1,3,5,7,5,11,17,15;
%e A256263 1,3,5,7,5,11,17,15,5,11,17,23,29,35,41,31;
%e A256263 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 A256263 ...
%e A256263 Right border gives A000225.
%e A256263 Apart from the initial 0 the row sums give A000302.
%e A256263 Rows converge to A256258.
%e A256263 .
%e A256263 Illustration of initial terms in the fourth quadrant of the square grid:
%e A256263 ---------------------------------------------------------------------------
%e A256263 n   a(n)                 Compact diagram
%e A256263 ---------------------------------------------------------------------------
%e A256263 0    0     _
%e A256263 1    1    |_|_ _
%e A256263 2    1      |_| |
%e A256263 3    3      |_ _|_ _ _ _
%e A256263 4    1          |_| | | |
%e A256263 5    3          |_ _| | |
%e A256263 6    5          |_ _ _| |
%e A256263 7    7          |_ _ _ _|_ _ _ _ _ _ _ _
%e A256263 8    1                  |_| | | |_ _  | |
%e A256263 9    3                  |_ _| | |_  | | |
%e A256263 10   5                  |_ _ _| | | | | |
%e A256263 11   7                  |_ _ _ _| | | | |
%e A256263 12   5                  | | |_ _ _| | | |
%e A256263 13  11                  | |_ _ _ _ _| | |
%e A256263 14  17                  |_ _ _ _ _ _ _| |
%e A256263 15  15                  |_ _ _ _ _ _ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A256263 16   1                                  |_| | | |_ _  | |_ _ _ _ _ _  | |
%e A256263 17   3                                  |_ _| | |_  | | |_ _ _ _ _  | | |
%e A256263 18   5                                  |_ _ _| | | | | |_ _ _ _  | | | |
%e A256263 19   7                                  |_ _ _ _| | | | |_ _ _  | | | | |
%e A256263 20   5                                  | | |_ _ _| | | |_ _  | | | | | |
%e A256263 21  11                                  | |_ _ _ _ _| | |_  | | | | | | |
%e A256263 22  17                                  |_ _ _ _ _ _ _| | | | | | | | | |
%e A256263 23  15                                  |_ _ _ _ _ _ _ _| | | | | | | | |
%e A256263 24   5                                  | | | | | | |_ _ _| | | | | | | |
%e A256263 25  11                                  | | | | | |_ _ _ _ _| | | | | | |
%e A256263 26  17                                  | | | | |_ _ _ _ _ _ _| | | | | |
%e A256263 27  23                                  | | | |_ _ _ _ _ _ _ _ _| | | | |
%e A256263 28  29                                  | | |_ _ _ _ _ _ _ _ _ _ _| | | |
%e A256263 29  35                                  | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e A256263 30  41                                  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
%e A256263 31  31                                  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e A256263 .
%e A256263 a(n) is also the number of cells in the n-th region of the diagram.
%e A256263 A256264(n) gives the total number of cells after n-th stage.
%t A256263 Flatten@Join[{0}, NestList[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 6]] (* _Ivan Neretin_, Feb 14 2017 *)
%Y A256263 Cf. A000225, A000302, A011782, A038573, A006257, A016969, A139251, A160552, A256250, A256258, A256260, A256261, A256264, A256265.
%K A256263 nonn,tabf,look
%O A256263 0,4
%A A256263 _Omar E. Pol_, Mar 30 2015
%E A256263 Terms a(95) to a(98) fixed by _Ivan Neretin_, Feb 14 2017