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Number of n X 3 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.
1

%I #7 Sep 07 2022 11:35:21

%S 5,57,2025,103373,6262064,404495219,26715084257,1777603386801,

%T 118573281463225,7915782848604211,528589085007311295,

%U 35300530985616790273,2357529150039721810029,157447991892723989479547

%N Number of n X 3 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

%C Column 3 of A209744.

%H R. H. Hardin, <a href="/A209739/b209739.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 100*a(n-1) -2365*a(n-2) +6020*a(n-3) +291532*a(n-4) -2681320*a(n-5) +4701820*a(n-6) +23602304*a(n-7) -82586672*a(n-8) +27026368*a(n-9) +113762816*a(n-10) -78159872*a(n-11) +7864320*a(n-12) for n>13.

%e Some solutions for n=5

%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0

%e ..1..2..1....1..2..3....1..2..1....1..2..1....1..2..1....1..2..1....1..2..1

%e ..0..0..0....3..1..1....1..0..0....0..0..1....3..3..1....2..0..0....3..3..2

%e ..1..3..4....4..3..0....1..2..3....1..2..1....0..1..2....0..3..4....2..4..2

%e ..1..5..3....5..3..1....0..0..3....0..0..0....0..3..1....0..5..4....0..0..2

%Y Cf. A209744.

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 12 2012