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A238287 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.

%I A238287 #6 Jul 23 2025 10:50:12
%S A238287 4,16,16,50,204,50,144,1844,1844,144,422,13948,42084,13948,422,1268,
%T A238287 105862,737366,737366,105862,1268,3823,850420,12926271,27913368,
%U A238287 12926271,850420,3823,11472,6953993,245920800,1058583000,1058583000,245920800
%N A238287 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.
%C A238287 Table starts
%C A238287 ......4.........16.............50................144.................422
%C A238287 .....16........204...........1844..............13948..............105862
%C A238287 .....50.......1844..........42084.............737366............12926271
%C A238287 ....144......13948.........737366...........27913368..........1058583000
%C A238287 ....422.....105862.......12926271.........1058583000.........87389474502
%C A238287 ...1268.....850420......245920800........44441926832.......8155057418133
%C A238287 ...3823....6953993.....4810332239......1931022884277.....790756782942944
%C A238287 ..11472...56279542....92790334588.....82508389421874...75089860262272452
%C A238287 ..34350..451637564..1767175335274...3470891253761820.7004416705370946171
%C A238287 .102896.3624058880.33631393265283.145872518046542058
%H A238287 R. H. Hardin, <a href="/A238287/b238287.txt">Table of n, a(n) for n = 1..97</a>
%F A238287 Empirical for column k:
%F A238287 k=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7)
%F A238287 k=2: [order 25]
%e A238287 Some solutions for n=3 k=4
%e A238287 ..0..2..2..1..1....2..2..1..0..0....0..2..2..0..0....0..0..2..2..0
%e A238287 ..0..2..2..1..0....0..0..0..0..0....0..2..2..0..0....0..0..2..2..0
%e A238287 ..1..2..2..2..0....0..0..0..1..1....1..3..3..2..0....0..2..2..3..3
%e A238287 ..1..2..2..2..1....2..2..0..3..3....1..3..3..3..0....2..3..3..3..3
%Y A238287 Column 1 is A203094(n+1)
%K A238287 nonn,tabl
%O A238287 1,1
%A A238287 _R. H. Hardin_, Feb 22 2014