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Number of (n+1) X 3 0..5 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
1

%I #11 Jun 05 2018 16:13:54

%S 4356,106596,2543436,60873876,1456391916,34845401556,833700866796,

%T 19946896311636,477243883220076,11418404289436116,273193561903563756,

%U 6536353100235366996,156386964438192169836,3741670970218511256276

%N Number of (n+1) X 3 0..5 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

%C Column 2 of A203934.

%H R. H. Hardin, <a href="/A203928/b203928.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 21*a(n-1) + 70*a(n-2).

%F Empirical g.f.: 36*x*(121 + 420*x) / (1 - 21*x - 70*x^2). - _Colin Barker_, Jun 05 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A203934.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2012