A196073 - OEIS

%I #8 May 08 2018 08:38:02

%S 0,2,1,1,6,8,12,28,36,63,147,216,400,746,1204,2234,4103,6927,12582,

%T 22430,38914,70334,124820,219139,392271,694562,1227704,2190008,

%U 3878528,6871416,12222729,21659291,38421292,68259422,121017534,214735198,381233984

%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,2,1,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 0's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 4's.

%C Column 3 of A196078.

%H R. H. Hardin, <a href="/A196073/b196073.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-2) +2*a(n-3) +a(n-4) +3*a(n-5) +6*a(n-6) -2*a(n-7) -7*a(n-8) -3*a(n-9) -4*a(n-10) -3*a(n-11) +a(n-12) +4*a(n-13) +a(n-14) +a(n-15) -2*a(n-17).

%F Empirical g.f.: x^2*(2 + x - x^2 + x^3 + 3*x^4 - 3*x^5 - 8*x^6 - 3*x^7 - 5*x^8 - 2*x^9 - x^10 + 6*x^11 + 2*x^13 - 2*x^15) / (1 - x^2 - 2*x^3 - x^4 - 3*x^5 - 6*x^6 + 2*x^7 + 7*x^8 + 3*x^9 + 4*x^10 + 3*x^11 - x^12 - 4*x^13 - x^14 - x^15 + 2*x^17). - _Colin Barker_, May 08 2018

%e All solutions for n=4:

%e ..0..1..0

%e ..1..3..1

%e ..1..3..1

%e ..0..1..0

%Y Cf. A196078.

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 27 2011