A256255 - OEIS

%I #21 Sep 26 2023 07:40:54

%S 1,1,7,1,7,13,19,1,7,13,19,25,31,37,43,1,7,13,19,25,31,37,43,49,55,61,

%T 67,73,79,85,91,1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103,

%U 109,115,121,127,133,139,145,151,157,163,169,175,181,187,1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103

%N Triangle read by rows: T(n,k) = 6*k + 1, n>=0, 0<=k<=(2^n-1).

%C Row n lists the first 2^n terms of A016921, n >= 0.

%C Row sums give A165665.

%C Right border gives A048488.

%C The sum of all terms of the first k rows gives A060867(k).

%C The product of the terms of the third row is equal to the Hardy-Ramanujan number: 1 * 7 * 13 * 19 = 1729.

%H Paolo Xausa, <a href="/A256255/b256255.txt">Table of n, a(n) for n = 0..16382</a> (rows 0..13 of the triangle, flattened)

%e Triangle begins:

%e 1;

%e 1,7;

%e 1,7,13,19;

%e 1,7,13,19,25,31,37,43;

%e 1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91;

%e ...

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

%e ------------------------------------------------------------------------

%e n   a(n)             Compact diagram

%e ------------------------------------------------------------------------

%e .            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

%e 0    1      |_|_  |_ _ _  |_ _ _ _ _ _ _  |

%e 1    1      | |_| |_ _  | |_ _ _ _ _ _  | |

%e 2    7      |_ _ _|_  | | |_ _ _ _ _  | | |

%e 3    1      | | | |_| | | |_ _ _ _  | | | |

%e 4    7      | | |_ _ _| | |_ _ _  | | | | |

%e 5   13      | |_ _ _ _ _| |_ _  | | | | | |

%e 6   19      |_ _ _ _ _ _ _|_  | | | | | | |

%e 7    1      | | | | | | | |_| | | | | | | |

%e 8    7      | | | | | | |_ _ _| | | | | | |

%e 9   13      | | | | | |_ _ _ _ _| | | | | |

%e 10  19      | | | | |_ _ _ _ _ _ _| | | | |

%e 11  25      | | | |_ _ _ _ _ _ _ _ _| | | |

%e 12  31      | | |_ _ _ _ _ _ _ _ _ _ _| | |

%e 13  37      | |_ _ _ _ _ _ _ _ _ _ _ _ _| |

%e 14  43      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

%e .

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

%e For other diagrams of the same family see A241717 and A256258.

%t With[{rows=7},Array[Range[1,6*2^#,6]&,rows,0]] (* _Paolo Xausa_, Sep 26 2023 *)

%Y Cf. A000225, A001235, A016921, A048488, A060867, A165665, A241717, A256258.

%K nonn,tabf

%O 0,3

%A _Omar E. Pol_, Apr 30 2015