Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Jan 20 2024 17:47:42
%S 0,4,4,24,80,24,108,768,768,108,432,6224,13904,6224,432,1620,46464,
%T 220968,220968,46464,1620,5832,330192,3277728,7002040,3277728,330192,
%U 5832,20412,2270592,46576336,208984848,208984848,46576336,2270592,20412
%N 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 Table starts
%C ......0.........4............24..............108.................432
%C ......4........80...........768.............6224...............46464
%C .....24.......768.........13904...........220968.............3277728
%C ....108......6224........220968..........7002040...........208984848
%C ....432.....46464.......3277728........208984848.........12637025328
%C ...1620....330192......46576336.......6004186984........738478504448
%C ...5832...2270592.....642676704.....167970539096......42119837369168
%C ..20412..15251152....8680278136....4607603633440....2359047063894464
%C ..69984.100647168..115349343264..124496158984840..130272136732736736
%C .236196.655139152.1513379596864.3323815506994632.7113223023541150960
%H R. H. Hardin, <a href="/A269152/b269152.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -9*a(n-2)
%F k=2: a(n) = 12*a(n-1) -38*a(n-2) +12*a(n-3) -a(n-4) for n>5
%F k=3: [order 8] for n>9
%F k=4: [order 20] for n>22
%F k=5: [order 42] for n>45
%e Some solutions for n=3, k=4
%e ..2..2..3..1. .0..2..2..2. .2..0..1..1. .0..3..3..1. .2..2..3..3
%e ..3..2..3..3. .3..3..3..2. .2..0..1..0. .1..1..3..1. .3..3..1..2
%e ..0..2..3..3. .3..2..2..2. .1..0..0..2. .3..3..3..1. .2..3..3..3
%Y Column 1 is A120908.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 20 2016