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A256258 Triangle read by rows in which the row lengths are the terms of A011782 and row n lists the terms of A016969 except for the right border which gives the positive terms of A000225.

%I A256258 #32 Feb 14 2017 15:16:47
%S A256258 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,
%T A256258 59,65,71,77,83,89,63,5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,
%U A256258 101,107,113,119,125,131,137,143,149,155,161,167,173,179,185,127,5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,131,137
%N A256258 Triangle read by rows in which the row lengths are the terms of A011782 and row n lists the terms of A016969 except for the right border which gives the positive terms of A000225.
%C A256258 Row sums give A002001.
%C A256258 The sum of all terms of first n rows gives A000302(n-1).
%C A256258 The rows of triangle A256263 converge to this sequence.
%C A256258 Rows converge to A016969.
%C A256258 First 11 terms agree with A151548.
%H A256258 Ivan Neretin, <a href="/A256258/b256258.txt">Table of n, a(n) for n = 1..8192</a>
%e A256258 Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
%e A256258 1;
%e A256258 3;
%e A256258 5,7;
%e A256258 5,11,17,15;
%e A256258 5,11,17,23,29,35,41,31;
%e A256258 5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,63;
%e A256258 5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,131,137,143,149,155,161,167,173,179,185,127;
%e A256258 ...
%e A256258 Illustration of initial terms in the fourth quadrant of the square grid:
%e A256258 ------------------------------------------------------------------------
%e A256258 n   a(n)             Compact diagram
%e A256258 ------------------------------------------------------------------------
%e A256258 .            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A256258 1    1      |_| | | |_ _  | |_ _ _ _ _ _  | |
%e A256258 2    3      |_ _| | |_  | | |_ _ _ _ _  | | |
%e A256258 3    5      |_ _ _| | | | | |_ _ _ _  | | | |
%e A256258 4    7      |_ _ _ _| | | | |_ _ _  | | | | |
%e A256258 5    5      | | |_ _ _| | | |_ _  | | | | | |
%e A256258 6   11      | |_ _ _ _ _| | |_  | | | | | | |
%e A256258 7   17      |_ _ _ _ _ _ _| | | | | | | | | |
%e A256258 8   15      |_ _ _ _ _ _ _ _| | | | | | | | |
%e A256258 9    5      | | | | | | |_ _ _| | | | | | | |
%e A256258 10  11      | | | | | |_ _ _ _ _| | | | | | |
%e A256258 11  17      | | | | |_ _ _ _ _ _ _| | | | | |
%e A256258 12  23      | | | |_ _ _ _ _ _ _ _ _| | | | |
%e A256258 13  29      | | |_ _ _ _ _ _ _ _ _ _ _| | | |
%e A256258 14  35      | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e A256258 15  41      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
%e A256258 16  31      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e A256258 .
%e A256258 a(n) is also the number of cells in the n-th region of the diagram.
%e A256258 It appears that A241717 can be represented by a similar diagram.
%t A256258 Nest[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 7] (* _Ivan Neretin_, Feb 14 2017 *)
%Y A256258 Cf. A000225, A000302, A002001, A011782, A016969, A141548, A241717, A256260, A256261, A256263, A256264.
%K A256258 nonn,tabf
%O A256258 1,2
%A A256258 _Omar E. Pol_, Apr 04 2015