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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

%I

%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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Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)