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Number of (n+1) X (1+1) 0..3 arrays with 2 X 2 edge jumps all no more than +1 in one of the clockwise or counterclockwise directions or both.
1

%I #9 Oct 16 2018 05:41:44

%S 110,1014,8968,80010,712722,6350732,56585338,504183278,4492335124,

%T 40027273406,356648038986,3177778909824,28314409931414,

%U 252284955262302,2247890695972232,20028988949649010,178460811756944538

%N Number of (n+1) X (1+1) 0..3 arrays with 2 X 2 edge jumps all no more than +1 in one of the clockwise or counterclockwise directions or both.

%H R. H. Hardin, <a href="/A234753/b234753.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) + 10*a(n-2) - 16*a(n-3) - 8*a(n-4) + 4*a(n-5) + a(n-6).

%F Empirical g.f.: 2*x*(55 + 67*x - 122*x^2 - 57*x^3 + 33*x^4 + 8*x^5) / (1 - 8*x - 10*x^2 + 16*x^3 + 8*x^4 - 4*x^5 - x^6). - _Colin Barker_, Oct 16 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A234760.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2013