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Number of (n+1) X (1+1) 0..5 arrays with every 2 X 2 subblock having the sum of the squares of all six edge and diagonal differences equal to 11.
1

%I #8 Oct 11 2018 14:08:56

%S 96,428,1824,8136,34848,155488,667200,2977440,12787200,57068480,

%T 245195520,1094334720,4702809600,20989561600,90210201600,402629644800,

%U 1730534860800,7723826124800,33198475776000,148173756672000

%N Number of (n+1) X (1+1) 0..5 arrays with every 2 X 2 subblock having the sum of the squares of all six edge and diagonal differences equal to 11.

%H R. H. Hardin, <a href="/A233811/b233811.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 30*a(n-2) - 220*a(n-4) + 240*a(n-6).

%F Empirical g.f.: 4*x*(24 + 107*x - 264*x^2 - 1176*x^3 + 312*x^4 + 1392*x^5) / (1 - 30*x^2 + 220*x^4 - 240*x^6). - _Colin Barker_, Oct 11 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 1 of A233818.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2013