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

Author

R. H. Hardin, Feb 21 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 1 is A120908.

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