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A269152 T(n,k) = Number of n X k 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.

%I A269152 #6 Jan 20 2024 17:47:42
%S A269152 0,4,4,24,80,24,108,768,768,108,432,6224,13904,6224,432,1620,46464,
%T A269152 220968,220968,46464,1620,5832,330192,3277728,7002040,3277728,330192,
%U A269152 5832,20412,2270592,46576336,208984848,208984848,46576336,2270592,20412
%N A269152 T(n,k) = Number of n X k 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.
%C A269152 Table starts
%C A269152 ......0.........4............24..............108.................432
%C A269152 ......4........80...........768.............6224...............46464
%C A269152 .....24.......768.........13904...........220968.............3277728
%C A269152 ....108......6224........220968..........7002040...........208984848
%C A269152 ....432.....46464.......3277728........208984848.........12637025328
%C A269152 ...1620....330192......46576336.......6004186984........738478504448
%C A269152 ...5832...2270592.....642676704.....167970539096......42119837369168
%C A269152 ..20412..15251152....8680278136....4607603633440....2359047063894464
%C A269152 ..69984.100647168..115349343264..124496158984840..130272136732736736
%C A269152 .236196.655139152.1513379596864.3323815506994632.7113223023541150960
%H A269152 R. H. Hardin, <a href="/A269152/b269152.txt">Table of n, a(n) for n = 1..220</a>
%F A269152 Empirical for column k:
%F A269152 k=1: a(n) = 6*a(n-1) -9*a(n-2)
%F A269152 k=2: a(n) = 12*a(n-1) -38*a(n-2) +12*a(n-3) -a(n-4) for n>5
%F A269152 k=3: [order 8] for n>9
%F A269152 k=4: [order 20] for n>22
%F A269152 k=5: [order 42] for n>45
%e A269152 Some solutions for n=3, k=4
%e A269152 ..2..2..3..1. .0..2..2..2. .2..0..1..1. .0..3..3..1. .2..2..3..3
%e A269152 ..3..2..3..3. .3..3..3..2. .2..0..1..0. .1..1..3..1. .3..3..1..2
%e A269152 ..0..2..3..3. .3..2..2..2. .1..0..0..2. .3..3..3..1. .2..3..3..3
%Y A269152 Column 1 is A120908.
%K A269152 nonn,tabl
%O A269152 1,2
%A A269152 _R. H. Hardin_, Feb 20 2016