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A228371 First differences of A228370. Also A001511 and A006519 interleaved. 6
1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 5, 16, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 6, 32, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 5, 16, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 4, 8, 1, 1, 2, 2, 1, 1, 3, 4, 1, 1, 2, 2, 1, 1, 7, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of toothpicks added at n-th stage to the toothpick structure (related to integer compositions) of A228370.

The equivalent sequence for integer partitions is A220517.

LINKS

Table of n, a(n) for n=1..128.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences

FORMULA

a(2n-1) = A001511(n), n >= 1. a(2n) = A006519(n), n >= 1.

EXAMPLE

Illustration of the structure after 32 stages. The diagram represents the 16 compositions of 5. The k-th horizontal line segment has length A001511(k) equals the largest part of the k-th region. The k-th vertical line segment has length A006519(k) equals the number of parts of the k-th region.

.      _ _ _ _ _

16     _        |

15     _|_      |

14     _  |     |

13     _|_|_    |

12     _    |   |

11     _|_  |   |

10     _  | |   |

9      _|_|_|_  |

8      _      | |

7      _|_    | |

6      _  |   | |

5      _|_|_  | |

4      _    | | |

3      _|_  | | |

2      _  | | | |

1       | | | | |

.

Written as an irregular triangle the sequence begins:

1,1;

2,2;

1,1,3,4;

1,1,2,2,1,1,4,8;

1,1,2,2,1,1,3,4,1,1,2,2,1,1,5,16;

1,1,2,2,1,1,3,4,1,1,2,2,1,1,4,8,1,1,2,2,1,1,3,4,1,1,2,2,1, 1,6,32;

1,1,2,2,1,1,3,4,1,1,2,2,1,1,4,8,1,1,2,2,1,1,3,4,1,1,2,2,1, 1,5,16,1,1,2,2,1,1,3,4,1,1,2,2,1,1,4,8,1,1,2,2,1,1,3,4,1, 1,2,2,1,1,7,64;

...

CROSSREFS

Row lengths give 2*A011782. Right border gives A000079.

Cf. A001511, A006519, A139250, A139251, A206437, A220517, A228370.

Sequence in context: A036064 A090706 A284548 * A176971 A247917 A050935

Adjacent sequences:  A228368 A228369 A228370 * A228372 A228373 A228374

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Aug 21 2013

STATUS

approved

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Last modified September 26 23:42 EDT 2021. Contains 347673 sequences. (Running on oeis4.)