A269289 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.

4, 16, 16, 60, 216, 64, 216, 2124, 2592, 256, 756, 19188, 62748, 29160, 1024, 2592, 164556, 1363572, 1698732, 314928, 4096, 8748, 1363572, 27788292, 87559668, 43674876, 3306744, 16384, 29160, 11026764, 544118148, 4204943820, 5306911092

Offset: 1

Author

R. H. Hardin, Feb 21 2016

Keywords

• nonn
• tabl

Comments

Table starts

......4.........16.............60...............216...................756

.....16........216...........2124.............19188................164556

.....64.......2592..........62748...........1363572..............27788292

....256......29160........1698732..........87559668............4204943820

...1024.....314928.......43674876........5306911092..........598478857956

...4096....3306744.....1085203980......309846524148........81907569617580

..16384...34012224....26317946844....17623065834612.....10908770041709316

..65536..344373768...626778812268...983118947312628...1424067311317705740

.262144.3443737680.14718495557052.54032675767734132.183070424003703987492

Examples

			Some solutions for n=3 k=4
..0..2..3..3. .0..2..3..1. .0..0..0..1. .0..2..2..2. .2..0..0..2
..2..1..3..1. .2..1..0..2. .2..2..3..1. .0..2..0..0. .0..0..3..3
..3..1..0..1. .1..0..2..0. .1..3..3..3. .2..0..0..2. .0..1..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A000302.

Column 2 is A159739(n+1).

Row 1 is A120926(n+1).

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: a(n) = 18*a(n-1) -81*a(n-2)

k=3: a(n) = 42*a(n-1) -441*a(n-2)

k=4: a(n) = 98*a(n-1) -2401*a(n-2) for n>3

k=5: a(n) = 234*a(n-1) -14277*a(n-2) +68796*a(n-3) -86436*a(n-4)

k=6: [order 6] for n>7

k=7: [order 10] for n>11

Empirical for row n:

n=1: a(n) = 6*a(n-1) -9*a(n-2)

n=2: a(n) = 14*a(n-1) -49*a(n-2) for n>4

n=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>7

n=4: [order 8] for n>12

n=5: [order 18] for n>23

n=6: [order 40] for n>46