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