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%I #50 Mar 12 2021 15:55:42
%S 1,2,6,15,44,126,374,1106,3307,9877,29599,88675,265932,797453,2392089,
%T 7175294,21525097,64572513,193715253,581137787,1743406694,5230197111,
%U 15690571861,47071649170,141214890563,423644479136,1270933270658,3812799252359,11438397268254,34315190174990
%N a(n) is the number of domino towers with n bricks up to horizontal flipping.
%C 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.
%C The number of domino towers with n bricks is given by 3^(n-1).
%H Andrew Howroyd, <a href="/A264746/b264746.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = (3^(n-1) + A320314(n))/2
%e For n=3, the a(3) = 6 domino towers are:
%e +-------+-------+-------+-------+
%e | | | | |
%e +-------+-------+-------+-------+
%e +-------+
%e | |
%e +---+---+---+---+
%e | | |
%e +-------+-------+
%e +-------+-------+
%e | | |
%e +---+---+---+---+
%e | |
%e +-------+
%e +-------+
%e | |
%e +-------+---+---+---+
%e | | |
%e +-------+-------+
%e +-------+
%e | |
%e +---+---+---+
%e | |
%e +---+---+---+
%e | |
%e +-------+
%e +-------+
%e | |
%e +---+---+---+
%e | |
%e +---+---+---+
%e | |
%e +-------+
%Y Cf. A000244, A168368, A320314.
%K nonn
%O 1,2
%A _Peter Kagey_, Oct 10 2018
%E Terms a(20) and beyond from _Andrew Howroyd_, Mar 12 2021