This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256264 #30 Feb 14 2017 15:16:34
%S A256264 0,1,2,5,6,9,14,21,22,25,30,37,42,53,70,85,86,89,94,101,106,117,134,
%T A256264 149,154,165,182,205,234,269,310,341,342,345,350,357,362,373,390,405,
%U A256264 410,421,438,461,490,525,566,597,602,613,630,653,682,717,758,805,858,917,982,1053,1130,1213,1302,1365
%N A256264 Partial sums of A256263.
%C A256264 First differs from A255747 at a(27).
%H A256264 Ivan Neretin, <a href="/A256264/b256264.txt">Table of n, a(n) for n = 0..8191</a>
%H A256264 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 A256264 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A256264 a(n) = (A256260(n+1) - 1)/4.
%e A256264 Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
%e A256264 0,
%e A256264 1,
%e A256264 2, 5,
%e A256264 6, 9, 14, 21,
%e A256264 22, 25, 30, 37, 42, 53, 70, 85;
%e A256264 86, 89, 94, 101, 106, 117, 134, 149, 154, 165, 182, 205, 234, 269,310,341;
%e A256264 ...
%e A256264 It appears that the first column gives 0 together with the terms of A047849, hence the right border gives A002450.
%e A256264 It appears that this triangle at least shares with the triangles from the following sequences; A151920, A255737, A255747, A256249, the positive elements of the columns k, if k is a power of 2.
%e A256264 From _Omar E. Pol, Jan 02 2016: (Start)
%e A256264 Illustration of initial terms in the fourth quadrant of the square grid:
%e A256264 ---------------------------------------------------------------------------
%e A256264 n a(n) Compact diagram
%e A256264 ---------------------------------------------------------------------------
%e A256264 0 0 _
%e A256264 1 1 |_|_ _
%e A256264 2 2 |_| |
%e A256264 3 5 |_ _|_ _ _ _
%e A256264 4 6 |_| | | |
%e A256264 5 9 |_ _| | |
%e A256264 6 14 |_ _ _| |
%e A256264 7 21 |_ _ _ _|_ _ _ _ _ _ _ _
%e A256264 8 22 |_| | | |_ _ | |
%e A256264 9 25 |_ _| | |_ | | |
%e A256264 10 30 |_ _ _| | | | | |
%e A256264 11 37 |_ _ _ _| | | | |
%e A256264 12 42 | | |_ _ _| | | |
%e A256264 13 53 | |_ _ _ _ _| | |
%e A256264 14 70 |_ _ _ _ _ _ _| |
%e A256264 15 85 |_ _ _ _ _ _ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A256264 16 86 |_| | | |_ _ | |_ _ _ _ _ _ | |
%e A256264 17 89 |_ _| | |_ | | |_ _ _ _ _ | | |
%e A256264 18 94 |_ _ _| | | | | |_ _ _ _ | | | |
%e A256264 19 101 |_ _ _ _| | | | |_ _ _ | | | | |
%e A256264 20 106 | | |_ _ _| | | |_ _ | | | | | |
%e A256264 21 117 | |_ _ _ _ _| | |_ | | | | | | |
%e A256264 22 134 |_ _ _ _ _ _ _| | | | | | | | | |
%e A256264 23 149 |_ _ _ _ _ _ _ _| | | | | | | | |
%e A256264 24 154 | | | | | | |_ _ _| | | | | | | |
%e A256264 25 165 | | | | | |_ _ _ _ _| | | | | | |
%e A256264 26 182 | | | | |_ _ _ _ _ _ _| | | | | |
%e A256264 27 205 | | | |_ _ _ _ _ _ _ _ _| | | | |
%e A256264 28 234 | | |_ _ _ _ _ _ _ _ _ _ _| | | |
%e A256264 29 269 | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e A256264 30 310 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
%e A256264 31 341 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e A256264 .
%e A256264 a(n) is also the total number of cells in the first n regions of the diagram. A256263(n) gives the number of cells in the n-th region of the diagram.
%e A256264 (End)
%t A256264 Accumulate@Flatten@Join[{0}, NestList[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 5]] (* _Ivan Neretin_, Feb 14 2017 *)
%Y A256264 Cf. A002450, A011782, A047849, A139250, A151920, A255737, A255747, A256249, A256258, A256260, A256261, A256263, A256265.
%K A256264 nonn,look
%O A256264 0,3
%A A256264 _Omar E. Pol_, Mar 30 2015