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A232076 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal, diagonal or antidiagonal neighbor, with top left element zero.

%I A232076 #6 Jul 23 2025 06:52:15
%S A232076 3,15,11,46,87,34,161,520,602,111,601,3681,6624,3985,361,2208,26587,
%T A232076 91636,82996,26713,1172,8053,189404,1313477,2265691,1043172,178484,
%U A232076 3809,29415,1348429,18480458,64298979,56126173,13105012,1193537,12377,107534
%N A232076 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal, diagonal or antidiagonal neighbor, with top left element zero.
%C A232076 Table starts
%C A232076 ......3........15...........46.............161................601
%C A232076 .....11........87..........520............3681..............26587
%C A232076 .....34.......602.........6624...........91636............1313477
%C A232076 ....111......3985........82996.........2265691...........64298979
%C A232076 ....361.....26713......1043172........56126173.........3154769585
%C A232076 ...1172....178484.....13105012......1389867384.......154723539035
%C A232076 ...3809...1193537....164650280.....34420057373......7588839921175
%C A232076 ..12377...7979619...2068621706....852404560481....372212311236497
%C A232076 ..40218..53352090..25989674166..21109624812630..18256039956940439
%C A232076 .130687.356709629.326528021922.522775448585677.895410839428587845
%H A232076 R. H. Hardin, <a href="/A232076/b232076.txt">Table of n, a(n) for n = 1..199</a>
%F A232076 Empirical for column k:
%F A232076 k=1: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F A232076 k=2: a(n) = 5*a(n-1) +11*a(n-2) +2*a(n-3) -8*a(n-5)
%F A232076 k=3: [order 10]
%F A232076 k=4: [order 30]
%F A232076 k=5: [order 50]
%F A232076 Empirical for row n:
%F A232076 n=1: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
%F A232076 n=2: [order 8]
%F A232076 n=3: [order 20]
%F A232076 n=4: [order 54]
%e A232076 Some solutions for n=3 k=4
%e A232076 ..0..0..1..1..0....0..0..1..1..1....0..0..0..1..1....0..1..0..0..1
%e A232076 ..0..0..0..0..0....1..1..0..0..0....0..0..0..1..0....1..0..0..1..1
%e A232076 ..0..0..1..1..1....1..0..0..0..0....0..0..0..0..0....1..1..0..0..1
%e A232076 ..1..1..1..1..1....0..0..1..1..1....1..1..1..1..0....1..0..0..1..0
%Y A232076 Column 1 is A180762(n+1)
%K A232076 nonn,tabl
%O A232076 1,1
%A A232076 _R. H. Hardin_, Nov 17 2013