A264746 a(n) is the number of domino towers with n bricks up to horizontal flipping.

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

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 A360274

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