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.

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, 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, 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

Offset

0,4

Comments

Partial sums give A256264.

First differs from A160552 at a(27).

Appears to be a canonical sequence partially related to the cellular automata of A139250, A147562, A162795, A169707, A255366, A256250. See also A256264 and A256260.

Links

Ivan Neretin, Table of n, a(n) for n = 0..8191

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to cellular automata

Example

Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
0;
1;
1,3;
1,3,5,7;
1,3,5,7,5,11,17,15;
1,3,5,7,5,11,17,15,5,11,17,23,29,35,41,31;
1,3,5,7,5,11,17,15,5,11,17,23,29,35,41,31,5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,63;
...
Right border gives A000225.
Apart from the initial 0 the row sums give A000302.
Rows converge to A256258.
.
Illustration of initial terms in the fourth quadrant of the square grid:
---------------------------------------------------------------------------
n   a(n)                 Compact diagram
---------------------------------------------------------------------------
0    0     _
1    1    |_|_ _
2    1      |_| |
3    3      |_ _|_ _ _ _
4    1          |_| | | |
5    3          |_ _| | |
6    5          |_ _ _| |
7    7          |_ _ _ _|_ _ _ _ _ _ _ _
8    1                  |_| | | |_ _  | |
9    3                  |_ _| | |_  | | |
10   5                  |_ _ _| | | | | |
11   7                  |_ _ _ _| | | | |
12   5                  | | |_ _ _| | | |
13  11                  | |_ _ _ _ _| | |
14  17                  |_ _ _ _ _ _ _| |
15  15                  |_ _ _ _ _ _ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
16   1                                  |_| | | |_ _  | |_ _ _ _ _ _  | |
17   3                                  |_ _| | |_  | | |_ _ _ _ _  | | |
18   5                                  |_ _ _| | | | | |_ _ _ _  | | | |
19   7                                  |_ _ _ _| | | | |_ _ _  | | | | |
20   5                                  | | |_ _ _| | | |_ _  | | | | | |
21  11                                  | |_ _ _ _ _| | |_  | | | | | | |
22  17                                  |_ _ _ _ _ _ _| | | | | | | | | |
23  15                                  |_ _ _ _ _ _ _ _| | | | | | | | |
24   5                                  | | | | | | |_ _ _| | | | | | | |
25  11                                  | | | | | |_ _ _ _ _| | | | | | |
26  17                                  | | | | |_ _ _ _ _ _ _| | | | | |
27  23                                  | | | |_ _ _ _ _ _ _ _ _| | | | |
28  29                                  | | |_ _ _ _ _ _ _ _ _ _ _| | | |
29  35                                  | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
30  41                                  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
31  31                                  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
.
a(n) is also the number of cells in the n-th region of the diagram.
A256264(n) gives the total number of cells after n-th stage.

Mathematica

Flatten@Join[{0}, NestList[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 6]] (* Ivan Neretin, Feb 14 2017 *)

Crossrefs

Cf. A000225, A000302, A011782, A038573, A006257, A016969, A139251, A160552, A256250, A256258, A256260, A256261, A256264, A256265.

Sequence in context: A179760 A334852 A160552 * A006257 A323555 A323553

Adjacent sequences: A256260 A256261 A256262 * A256264 A256265 A256266

Keyword

nonn,tabf,look

Author

Omar E. Pol, Mar 30 2015

Extensions

Terms a(95) to a(98) fixed by Ivan Neretin, Feb 14 2017

Status

approved