A269276 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

0, 4, 0, 24, 108, 0, 108, 1368, 1620, 0, 432, 13896, 46872, 20412, 0, 1620, 127512, 1104264, 1365336, 236196, 0, 5832, 1104264, 23549400, 74853576, 36673560, 2598156, 0, 20412, 9211608, 474819408, 3719884392, 4684312584, 938176344

Offset

1,2

Comments

Table starts

.0........4..........24............108...............432................1620

.0......108........1368..........13896............127512.............1104264

.0.....1620.......46872........1104264..........23549400...........474819408

.0....20412.....1365336.......74853576........3719884392........174924572760

.0...236196....36673560.....4684312584......542973139128......59587625651904

.0..2598156...938176344...279339197256....75556007986536...19356924219624936

.0.27634932.23230366488.16128206816904.10181956012212600.6090616046325570480

Links

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

Formula

Empirical for column k:

k=1: a(n) = 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..0..1. .0..0..0..0. .0..2..0..0. .0..0..0..0. .0..0..2..0
..0..2..3..1. .2..2..0..0. .2..2..3..1. .2..0..2..1. .0..2..2..3
..2..1..0..2. .3..2..1..1. .0..1..0..2. .0..0..1..3. .3..1..1..0

Crossrefs

Row 1 is A120908.

Sequence in context: A357810 A057402 A269214 * A359521 A172394 A172395

Adjacent sequences: A269273 A269274 A269275 * A269277 A269278 A269279

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 21 2016

Status

approved