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A256264 Partial sums of A256263. 8
0, 1, 2, 5, 6, 9, 14, 21, 22, 25, 30, 37, 42, 53, 70, 85, 86, 89, 94, 101, 106, 117, 134, 149, 154, 165, 182, 205, 234, 269, 310, 341, 342, 345, 350, 357, 362, 373, 390, 405, 410, 421, 438, 461, 490, 525, 566, 597, 602, 613, 630, 653, 682, 717, 758, 805, 858, 917, 982, 1053, 1130, 1213, 1302, 1365 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

First differs from A255747 at a(27).

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

FORMULA

a(n) = (A256260(n+1) - 1)/4.

EXAMPLE

Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:

0,

1,

2,   5,

6,   9, 14,  21,

22, 25, 30,  37,  42,  53,  70,  85;

86, 89, 94, 101, 106, 117, 134, 149, 154, 165, 182, 205, 234, 269,310,341;

...

It appears that the first column gives 0 together with the terms of A047849, hence the right border gives A002450.

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.

From _Omar E. Pol, Jan 02 2016: (Start)

Illustration of initial terms in the fourth quadrant of the square grid:

---------------------------------------------------------------------------

n    a(n)                 Compact diagram

---------------------------------------------------------------------------

0     0     _

1     1    |_|_ _

2     2      |_| |

3     5      |_ _|_ _ _ _

4     6          |_| | | |

5     9          |_ _| | |

6    14          |_ _ _| |

7    21          |_ _ _ _|_ _ _ _ _ _ _ _

8    22                  |_| | | |_ _  | |

9    25                  |_ _| | |_  | | |

10   30                  |_ _ _| | | | | |

11   37                  |_ _ _ _| | | | |

12   42                  | | |_ _ _| | | |

13   53                  | |_ _ _ _ _| | |

14   70                  |_ _ _ _ _ _ _| |

15   85                  |_ _ _ _ _ _ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

16   86                                  |_| | | |_ _  | |_ _ _ _ _ _  | |

17   89                                  |_ _| | |_  | | |_ _ _ _ _  | | |

18   94                                  |_ _ _| | | | | |_ _ _ _  | | | |

19  101                                  |_ _ _ _| | | | |_ _ _  | | | | |

20  106                                  | | |_ _ _| | | |_ _  | | | | | |

21  117                                  | |_ _ _ _ _| | |_  | | | | | | |

22  134                                  |_ _ _ _ _ _ _| | | | | | | | | |

23  149                                  |_ _ _ _ _ _ _ _| | | | | | | | |

24  154                                  | | | | | | |_ _ _| | | | | | | |

25  165                                  | | | | | |_ _ _ _ _| | | | | | |

26  182                                  | | | | |_ _ _ _ _ _ _| | | | | |

27  205                                  | | | |_ _ _ _ _ _ _ _ _| | | | |

28  234                                  | | |_ _ _ _ _ _ _ _ _ _ _| | | |

29  269                                  | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |

30  310                                  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |

31  341                                  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

.

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.

(End)

MATHEMATICA

Accumulate@Flatten@Join[{0}, NestList[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 5]] (* Ivan Neretin, Feb 14 2017 *)

CROSSREFS

Cf. A002450, A011782, A047849, A139250, A151920, A255737, A255747, A256249, A256258, A256260, A256261, A256263, A256265.

Sequence in context: A163782 A226793 A255747 * A256249 A169779 A326118

Adjacent sequences:  A256261 A256262 A256263 * A256265 A256266 A256267

KEYWORD

nonn,look

AUTHOR

Omar E. Pol, Mar 30 2015

STATUS

approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)