cp's OEIS Frontend

A197884 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

%I A197884 #13 Jun 02 2025 05:12:40
%S A197884 1,3,6,47,77,196,529,1637,4235,11211,30271,83254,225148,606579,
%T A197884 1638498,4440639,12016918,32485381,87846790,237662631,642926239,
%U A197884 1738933011,4703362637,12722244082,34413103568,93083202626,251777401480
%N A197884 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.
%C A197884 Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's.
%H A197884 R. H. Hardin, <a href="/A197884/b197884.txt">Table of n, a(n) for n = 1..200</a>
%H A197884 Robert Israel, <a href="/A197884/a197884.pdf">Maple-assisted proof of formula</a>
%F A197884 Empirical: a(n) = a(n-1) +a(n-2) +4*a(n-3) +12*a(n-4) +7*a(n-5) +21*a(n-6) -22*a(n-7) -6*a(n-8) -64*a(n-9) -136*a(n-10) +16*a(n-11) +112*a(n-12) +621*a(n-13) +473*a(n-14) +396*a(n-15) -294*a(n-16) -1044*a(n-17) -744*a(n-18) -475*a(n-19) +1462*a(n-20) +156*a(n-21) -1601*a(n-22) -627*a(n-23) -2504*a(n-24) -1566*a(n-25) +468*a(n-26) -518*a(n-27) +384*a(n-28) +444*a(n-29) +208*a(n-30) +400*a(n-31) +96*a(n-32).
%F A197884 Empirical formula verified: see link. - _Robert Israel_, Aug 24 2018
%e A197884 Some solutions for n=4
%e A197884 ..1..2..0....1..1..0....1..1..2....0..1..1....2..1..0....0..1..2....0..1..2
%e A197884 ..0..1..1....2..2..1....2..3..1....1..2..2....1..1..2....1..0..1....1..4..1
%e A197884 ..1..1..2....1..0..1....1..1..3....1..3..1....1..4..1....2..2..1....2..1..1
%e A197884 ..2..1..0....0..1..2....0..2..1....2..1..0....2..1..0....1..1..0....0..1..2
%Y A197884 Column 3 of A197889.
%K A197884 nonn
%O A197884 1,2
%A A197884 _R. H. Hardin_, Oct 19 2011