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Number of (n+1) X 4 0..5 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
1

%I #11 Jun 05 2018 16:14:09

%S 47916,2543436,140120856,7748585676,428652828396,23714024087016,

%T 1311917257647036,72578467770478956,4015218299044750776,

%U 222131694756911277996,12288868539361015411116,679850257967547125048136

%N Number of (n+1) X 4 0..5 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

%C Column 3 of A203934.

%H R. H. Hardin, <a href="/A203929/b203929.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 61*a(n-1) - 315*a(n-2) + 50*a(n-3).

%F Empirical g.f.: 36*x*(1331 - 10540*x + 1800*x^2) / (1 - 61*x + 315*x^2 - 50*x^3). - _Colin Barker_, Jun 05 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A203934.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2012