cp's OEIS Frontend

A230675 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).

%I A230675 #6 Jun 02 2025 08:45:18
%S A230675 0,3,0,3,15,0,9,87,81,0,15,513,1173,423,0,33,3387,18915,17271,2247,0,
%T A230675 63,21933,340563,730503,251595,11925,0,129,141411,6081561,37034355,
%U A230675 28368687,3669765,63291,0,255,913245,108108231,1844154933,4022141121,1100265795
%N A230675 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value 2-x(i,j).
%C A230675 Table starts
%C A230675 .0......3.........3.............9...............15...................33
%C A230675 .0.....15........87...........513.............3387................21933
%C A230675 .0.....81......1173.........18915...........340563..............6081561
%C A230675 .0....423.....17271........730503.........37034355...........1844154933
%C A230675 .0...2247....251595......28368687.......4022141121.........559929294657
%C A230675 .0..11925...3669765....1100265795.....436827078531......169908632412447
%C A230675 .0..63291..53519163...42681522741...47444197636239....51564141085334199
%C A230675 .0.335943.780527655.1655698076319.5152946201086569.15648664251672721725
%H A230675 R. H. Hardin, <a href="/A230675/b230675.txt">Table of n, a(n) for n = 1..126</a>
%F A230675 Empirical for column k:
%F A230675 k=1: a(n) = a(n-1)
%F A230675 k=2: a(n) = 5*a(n-1) +2*a(n-2) -a(n-3) -5*a(n-4)
%F A230675 k=3: a(n) = 14*a(n-1) +9*a(n-2) -9*a(n-3) +30*a(n-4) -19*a(n-5)
%F A230675 k=4: [order 32]
%F A230675 k=5: [order 80]
%F A230675 Empirical for row n:
%F A230675 n=1: a(n) = a(n-1) +2*a(n-2)
%F A230675 n=2: a(n) = 5*a(n-1) +6*a(n-2) +20*a(n-3) +12*a(n-4) +8*a(n-5)
%F A230675 n=3: [order 15] for n>16
%F A230675 n=4: [order 64] for n>65
%e A230675 Some solutions for n=3 k=4
%e A230675 ..0..2..0..2....2..0..0..2....2..0..1..2....0..0..0..2....1..1..1..1
%e A230675 ..0..0..1..1....0..1..0..2....1..1..0..1....2..2..0..1....1..2..1..2
%e A230675 ..2..2..0..1....1..2..1..2....1..1..1..2....2..0..1..2....2..0..0..2
%Y A230675 Column 2 is A229841
%Y A230675 Row 1 is A062510(n-1)
%K A230675 nonn,tabl
%O A230675 1,2
%A A230675 _R. H. Hardin_, Oct 27 2013