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Number of 2Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.
1

%I #9 Nov 04 2024 02:42:02

%S 1,14,74,296,1130,4682,19448,79592,326810,1343042,5516132,22658744,

%T 93073958,382310690,1570402928,6450645104,26496901994,108839752922,

%U 447074397188,1836420218672,7543351642070,30985365821066,127276699845344,522806747988728,2147501432084138

%N Number of 2Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

%C Row 2 of A232376.

%H R. H. Hardin, <a href="/A232377/b232377.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +a(n-2) +13*a(n-3) +26*a(n-5) -4*a(n-6) +24*a(n-7) +16*a(n-8) for n>9.

%F Empirical g.f.: x + 2*x^2*(-7 -16*x -30*x^2 +7*x^3 -17*x^4 -30*x^5 -4*x^6 +8*x^7) / ( (2*x^2+1)*(8*x^6 +12*x^5 -6*x^4 +7*x^3 +3*x^2 +3*x-1) ). - _R. J. Mathar_, Nov 27 2013

%e Some solutions for n=7

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 23 2013