A196436 - OEIS

%I #8 Nov 20 2014 19:24:48

%S 1,2,2,3,5,3,4,9,9,4,6,20,25,20,6,9,41,75,75,41,9,13,85,213,314,213,

%T 85,13,19,178,621,1283,1283,621,178,19,28,369,1801,5311,7358,5311,

%U 1801,369,28,41,769,5219,21803,42604,42604,21803,5219,769,41,60,1600,15133,89640

%N T(n,k) = Number of n X k 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,1,0,3,4 for x=0,1,2,3,4.

%C Every 0 is next to zero 2's, every 1 is next to one 1's, every 2 is next to two 2's, every 3 is next to three 3's, every 4 is next to four 4's.

%C Table starts:

%C ..1....2.....3.......4........6..........9..........13............19

%C ..2....5.....9......20.......41.........85.........178...........369

%C ..3....9....25......75......213........621........1801..........5219

%C ..4...20....75.....314.....1283.......5311.......21803.........89640

%C ..6...41...213....1283.....7358......42604......246463.......1427278

%C ..9...85...621....5311....42604.....349511.....2856711......23313460

%C .13..178..1801...21803...246463....2856711....32855368.....378154308

%C .19..369..5219...89640..1427278...23313460...378154308....6141909014

%C .28..769.15133..369032..8257394..190423461..4356726770...99754551113

%C .41.1600.43867.1517961.47782109.1555501171.50163397373.1619739781963

%H R. H. Hardin, <a href="/A196436/b196436.txt">Table of n, a(n) for n = 1..420</a>

%e Some solutions for n=6, k=4:

%e ..0..0..1..1....1..0..1..1....0..1..0..0....0..0..0..0....1..1..0..0

%e ..0..1..0..0....1..0..0..0....0..1..0..0....0..0..1..1....0..0..1..1

%e ..0..1..0..1....0..1..0..1....0..0..0..0....0..0..0..0....0..0..0..0

%e ..0..0..0..1....0..1..0..1....0..0..0..0....0..0..0..0....0..0..0..0

%e ..0..0..0..0....1..0..0..0....1..1..0..0....0..0..1..1....1..1..0..0

%e ..1..1..0..0....1..0..1..1....0..0..0..0....0..0..0..0....0..0..1..1

%Y Column 1 is A000930(n+1).

%Y Column 2 is A105309(n+1).

%Y Diagonal is A145773.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Oct 02 2011