A269194 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

4, 16, 16, 60, 108, 60, 216, 708, 708, 216, 756, 4476, 9284, 4476, 756, 2592, 27684, 115452, 115452, 27684, 2592, 8748, 168252, 1399612, 2817548, 1399612, 168252, 8748, 29160, 1008804, 16629436, 67134380, 67134380, 16629436, 1008804, 29160

Offset

1,1

Comments

Table starts

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

.....16.......108..........708............4476..............27684

.....60.......708.........9284..........115452............1399612

....216......4476.......115452.........2817548...........67134380

....756.....27684......1399612........67134380.........3159954052

...2592....168252.....16629436......1567933676.......145995171708

...8748...1008804....194596516.....36068275268......6648192704604

..29160...5983164...2249848972....819789099172....299224791093196

..96228..35170980..25758552060..18452018423420..13339889117822420

.314928.205214268.292530733516.411983259384452.590022908205332548

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

k=2: a(n) = 10*a(n-1) -21*a(n-2) -20*a(n-3) -4*a(n-4) for n>5

k=3: [order 8] for n>9

k=4: [order 16] for n>17

k=5: [order 40] for n>41

Example

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

Crossrefs

Column 1 is A120926(n+1).

Sequence in context: A207283 A207479 A207535 * A269143 A269109 A269201

Adjacent sequences: A269191 A269192 A269193 * A269195 A269196 A269197

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2016

Status

approved