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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000302.

Column 2 is A159739(n+1).

Row 1 is A120926(n+1).

Sequence in context: A269143 A269109 A269201 * A267933 A206974 A206577

Adjacent sequences: A269286 A269287 A269288 * A269290 A269291 A269292

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 21 2016

Status

approved