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A264746 a(n) is the number of domino towers with n bricks up to horizontal flipping. 3
1, 2, 6, 15, 44, 126, 374, 1106, 3307, 9877, 29599, 88675, 265932, 797453, 2392089, 7175294, 21525097, 64572513, 193715253, 581137787, 1743406694, 5230197111, 15690571861, 47071649170, 141214890563, 423644479136, 1270933270658, 3812799252359, 11438397268254, 34315190174990 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A domino tower is a stack of bricks, where (1) each row is offset from the preceding row by half of a brick, (2) the bottom row is contiguous, and (3) each brick is supported from below by at least half of a brick.

The number of domino towers with n bricks is given by 3^(n-1).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = (3^(n-1) + A320314(n))/2

EXAMPLE

For n=3, the a(3) = 6 domino towers are:

+-------+-------+-------+-------+

|       |       |       |       |

+-------+-------+-------+-------+

    +-------+

    |       |

+---+---+---+---+

|       |       |

+-------+-------+

+-------+-------+

|       |       |

+---+---+---+---+

    |       |

    +-------+

            +-------+

            |       |

+-------+---+---+---+

|       |       |

+-------+-------+

    +-------+

    |       |

+---+---+---+

|       |

+---+---+---+

    |       |

    +-------+

        +-------+

        |       |

    +---+---+---+

    |       |

+---+---+---+

|       |

+-------+

CROSSREFS

Cf. A000244, A168368, A320314.

Sequence in context: A148438 A148439 A151515 * A052870 A293743 A001444

Adjacent sequences:  A264743 A264744 A264745 * A264747 A264748 A264749

KEYWORD

nonn

AUTHOR

Peter Kagey, Oct 10 2018

EXTENSIONS

Terms a(20) and beyond from Andrew Howroyd, Mar 12 2021

STATUS

approved

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Last modified April 19 22:40 EDT 2021. Contains 343117 sequences. (Running on oeis4.)