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A233776 Number of grid points that are covered on the semi-infinite hexagonal grid after n-th stage in a cellular automaton in which the toothpicks are connected by their endpoints but the toothpicks placed in northwest or northeast direction are prohibited, starting with a(0) = 1. 1
1, 2, 4, 6, 9, 11, 15, 19, 24, 26, 30, 34, 40, 44, 52, 60, 69, 71, 75, 79, 85, 89, 97, 105, 115, 119, 127, 135, 147, 155, 171, 187, 204, 206, 210, 214, 220, 224, 232, 240, 250, 254, 262, 270, 282, 290, 306, 322, 340, 344, 352, 360, 372, 380, 396, 412, 432, 440, 456, 472, 496 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the number of grid points that are covered on the semi-infinite square grid after n-th stage in a D-toothpick structure in which the toothpicks placed in horizontal direction are prohibited, starting with a(0) = 1.

Note that both the structure mentioned in the above comment and the structure mentioned in the definition are essentially equivalents. Both structures are related to the Sierpinski triangle (see A047999). The number of edges in the structure after n-th stage is A006046(n). The number of edges added at n-th stage is A001316(n-1), for n >= 1 (see example).

LINKS

Table of n, a(n) for n=0..60.

Omar E. Pol, Illustration of the structure on the square grid after 32 stages

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

Index entries for sequences related to toothpick sequences

EXAMPLE

Illustration of initial terms:

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

. A001316 A006046         Diagram         A233777   a(n)

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

.            0

.                            *               1       1

.    1       1               |

.                            *               1       2

.    2       3              / \

.                          *   *             2       4

.    2       5             |   |

.                          *   *             2       6

.    4       9            / \ / \

.                        *   *   *           3       9

.    2      11           |       |

.                        *       *           2      11

.    4      15          / \     / \

.                      *   *   *   *         4      15

.    4      19         |   |   |   |

.                      *   *   *   *         4      19

.    8      27        / \ / \ / \ / \

.                    *   *   *   *   *       5      24

.    2      29       |               |

.                    *               *       2      26

.    4      33      / \             / \

.                  *   *           *   *     4      30

.

CROSSREFS

Partial sums of A233777.

Cf. A001316, A006046, A047999, A139250, A141614, A160120, A160128, A160425, A194270, A194440, A233774.

Sequence in context: A300416 A038107 A303331 * A195526 A153196 A247185

Adjacent sequences:  A233773 A233774 A233775 * A233777 A233778 A233779

KEYWORD

nonn

AUTHOR

Omar E. Pol, Dec 25 2013

STATUS

approved

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)