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

Author

Peter Kagey, Oct 10 2018

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

Cf. A000244, A168368, A320314.

Formula

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

Extensions

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