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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. 6
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, 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, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums give A002001.

The sum of all terms of first n rows gives A000302(n-1).

The rows of triangle A256263 converge to this sequence.

Rows converge to A016969.

First 11 terms agree with A151548.

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..8192

EXAMPLE

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

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;

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;

...

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

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

n   a(n)             Compact diagram

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

.            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1    1      |_| | | |_ _  | |_ _ _ _ _ _  | |

2    3      |_ _| | |_  | | |_ _ _ _ _  | | |

3    5      |_ _ _| | | | | |_ _ _ _  | | | |

4    7      |_ _ _ _| | | | |_ _ _  | | | | |

5    5      | | |_ _ _| | | |_ _  | | | | | |

6   11      | |_ _ _ _ _| | |_  | | | | | | |

7   17      |_ _ _ _ _ _ _| | | | | | | | | |

8   15      |_ _ _ _ _ _ _ _| | | | | | | | |

9    5      | | | | | | |_ _ _| | | | | | | |

10  11      | | | | | |_ _ _ _ _| | | | | | |

11  17      | | | | |_ _ _ _ _ _ _| | | | | |

12  23      | | | |_ _ _ _ _ _ _ _ _| | | | |

13  29      | | |_ _ _ _ _ _ _ _ _ _ _| | | |

14  35      | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |

15  41      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |

16  31      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

.

a(n) is also the number of cells in the n-th region of the diagram.

It appears that A241717 can be represented by a similar diagram.

MATHEMATICA

Nest[Join[#, Range[Length[#] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 7] (* Ivan Neretin, Feb 14 2017 *)

CROSSREFS

Cf. A000225, A000302, A002001, A011782, A016969, A141548, A241717, A256260, A256261, A256263, A256264.

Sequence in context: A073409 A260234 A151548 * A177433 A264827 A214091

Adjacent sequences:  A256255 A256256 A256257 * A256259 A256260 A256261

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 04 2015

STATUS

approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)