A269201 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three no more than once.

4, 16, 16, 60, 180, 64, 216, 1284, 1740, 256, 756, 9612, 25572, 15540, 1024, 2592, 68052, 400428, 471492, 132300, 4096, 8748, 472044, 5877228, 15289548, 8314020, 1090740, 16384, 29160, 3212820, 84310620, 463790340, 555862380, 142233732

Offset

1,1

Comments

Table starts

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

......16........180...........1284..............9612................68052

......64.......1740..........25572............400428..............5877228

.....256......15540.........471492..........15289548............463790340

....1024.....132300........8314020.........555862380..........34838403756

....4096....1090740......142233732.......19558138380........2532677348772

...16384....8787660.....2380537188......672230393004......179867149105740

...65536...69580980....39186271044....22702294138188....12551707872624132

..262144..543538380...636703584804...756261535626732...864008559706781292

.1048576.4200069300.10237337586180.24917784636315276.58827234014669683044

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

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

k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3

k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5

k=4: [order 6] for n>7

k=5: [order 20] for n>21

k=6: [order 42] for n>43

Empirical for row n:

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

n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)

n=3: [order 8]

n=4: [order 20]

n=5: [order 52] for n>53

Example

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

Crossrefs

Column 1 is A000302.

Column 2 is A269103.

Row 1 is A120926(n+1).

Sequence in context: A269194 A269143 A269109 * A269289 A267933 A206974

Adjacent sequences: A269198 A269199 A269200 * A269202 A269203 A269204

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2016

Status

approved