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A196954 Number of n X 5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,3,4,0 for x=0,1,2,3,4.

%I A196954 #9 Jun 19 2025 20:40:38
%S A196954 6,41,282,2687,23956,214124,1918608,17197531,154075730,1380294235,
%T A196954 12367225355,110805484184,992753872004,8894587877534,79691287683196,
%U A196954 713994702986579,6397041470072060,57314366530825786,513508682261967861
%N A196954 Number of n X 5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,3,4,0 for x=0,1,2,3,4.
%C A196954 Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 3's, every 3 is next to 3 4's, every 4 is next to 4 0's.
%C A196954 Column 5 of A196957.
%H A196954 R. H. Hardin, <a href="/A196954/b196954.txt">Table of n, a(n) for n = 1..210</a>
%F A196954 Empirical: a(n) = 3*a(n-1) +30*a(n-2) +172*a(n-3) +401*a(n-4) -187*a(n-5) -3185*a(n-6) -3461*a(n-7) +7148*a(n-8) +9487*a(n-9) -10397*a(n-10) -9254*a(n-11) +6040*a(n-12) +16653*a(n-13) +10403*a(n-14) -6166*a(n-15) -32205*a(n-16) +88763*a(n-17) -92837*a(n-18) +107224*a(n-19) -129392*a(n-20) +84460*a(n-21) -49775*a(n-22) +24488*a(n-23) -13127*a(n-24) +3256*a(n-25) +696*a(n-26) +1437*a(n-27) -1138*a(n-28) +549*a(n-29) -209*a(n-30) +72*a(n-31) -129*a(n-32) +54*a(n-33) -6*a(n-34) +4*a(n-35) -a(n-36) for n>37.
%e A196954 Some solutions for n=4
%e A196954 ..0..1..1..0..0....0..1..1..0..0....1..1..0..1..0....0..0..0..0..0
%e A196954 ..0..0..0..0..0....0..0..0..4..0....0..0..0..1..0....0..0..0..1..1
%e A196954 ..0..0..0..1..1....0..1..1..0..0....0..0..0..0..0....1..1..0..0..0
%e A196954 ..1..1..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..1..1
%Y A196954 Cf. A196957.
%K A196954 nonn
%O A196954 1,1
%A A196954 _R. H. Hardin_, Oct 08 2011