A196957 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,1,3,4,0 for x=0,1,2,3,4.

1, 2, 2, 3, 5, 3, 4, 9, 9, 4, 6, 20, 26, 20, 6, 9, 41, 87, 87, 41, 9, 13, 85, 282, 492, 282, 85, 13, 19, 178, 919, 2687, 2687, 919, 178, 19, 28, 369, 2987, 14509, 23956, 14509, 2987, 369, 28, 41, 769, 9722, 78717, 214124, 214124, 78717, 9722, 769, 41, 60, 1600, 31643

Offset: 1

Author

R. H. Hardin Oct 08 2011

Keywords

• nonn
• tabl

Comments

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 3's, every 3 is next to 3 4's, every 4 is next to 4 0's

Table starts

..1....2......3........4..........6............9.............13

..2....5......9.......20.........41...........85............178

..3....9.....26.......87........282..........919...........2987

..4...20.....87......492.......2687........14509..........78717

..6...41....282.....2687......23956.......214124........1918608

..9...85....919....14509.....214124......3166711.......46887039

.13..178...2987....78717....1918608.....46887039.....1147966466

.19..369...9722...427700...17197531....695103098....28133304588

.28..769..31643..2320738..154075730..10297360567...688970472958

.41.1600.102962.12593583.1380294235.152533682507.16871844816740

Examples

			Some solutions for n=6 k=4
..0..0..0..0....0..1..0..0....1..1..0..0....0..1..0..0....0..0..0..0
..1..0..1..1....0..1..0..0....0..0..1..1....0..1..0..0....0..0..1..0
..1..0..0..0....0..0..0..0....1..1..0..0....1..0..0..0....0..0..1..0
..0..0..1..1....0..0..0..0....0..0..4..0....1..0..4..0....0..0..0..1
..1..0..0..0....0..1..0..0....0..0..0..0....0..4..0..0....1..1..0..1
..1..0..0..0....0..1..0..0....0..1..1..0....0..0..1..1....0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..364

Crossrefs

Column 1 is A000930(n+1)

Column 2 is A105309(n+1)