The On-Line Encyclopedia of Integer Sequences (OEIS)

A256255 revision #14

A256255

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

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

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OFFSET

0,3

COMMENTS

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

Row sums give A165665.

Right border gives A048488.

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

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

LINKS

Table of n, a(n) for n=0..80.

EXAMPLE

Triangle begins:

1,7;

1,7,13,19;

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

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

...

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

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

n a(n) Compact diagram

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

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

0 1 |_|_ |_ _ _ |_ _ _ _ _ _ _ |

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

2 7 |_ _ _|_ | | |_ _ _ _ _ | | |

3 1 | | | |_| | | |_ _ _ _ | | | |

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

5 13 | |_ _ _ _ _| |_ _ | | | | | |

6 19 |_ _ _ _ _ _ _|_ | | | | | | |

7 1 | | | | | | | |_| | | | | | | |

8 7 | | | | | | |_ _ _| | | | | | |

9 13 | | | | | |_ _ _ _ _| | | | | |

10 19 | | | | |_ _ _ _ _ _ _| | | | |

11 25 | | | |_ _ _ _ _ _ _ _ _| | | |

12 31 | | |_ _ _ _ _ _ _ _ _ _ _| | |

13 37 | |_ _ _ _ _ _ _ _ _ _ _ _ _| |

14 43 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

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

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

CROSSREFS

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

Sequence in context: A081776 A354128 A377188 * A131115 A151778 A138616

Adjacent sequences: A256252 A256253 A256254 * A256256 A256257 A256258

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 30 2015

STATUS

editing