A233982 - OEIS

A233982

Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 10, and no two adjacent values equal.

%I #7 Oct 12 2018 10:49:41

%S 56,236,976,4064,16880,70176,291648,1212224,5038336,20941056,87037696,

%T 361757184,1503580160,6249368576,25974407168,107958083584,

%U 448708898816,1864980094976,7751463714816,32217603784704,133906837667840

%N Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 10, and no two adjacent values equal.

%H R. H. Hardin, <a href="/A233982/b233982.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 8*a(n-2) + 4*a(n-3).

%F Empirical g.f.: 4*x*(14 + 31*x + 14*x^2) / (1 - 2*x - 8*x^2 - 4*x^3). - _Colin Barker_, Oct 12 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 1 of A233989.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 18 2013