A268904 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

0, 3, 0, 12, 36, 0, 36, 168, 240, 0, 96, 696, 1584, 1344, 0, 240, 2664, 9720, 12960, 6912, 0, 576, 9720, 54936, 118584, 98496, 33792, 0, 1344, 34344, 299088, 1004184, 1347192, 715392, 159744, 0, 3072, 118584, 1585800, 8250912, 17194680, 14644152, 5038848

Offset: 1

Author

R. H. Hardin, Feb 15 2016

Keywords

• nonn
• tabl

Comments

Table starts

.0.......3........12..........36............96............240..............576

.0......36.......168.........696..........2664...........9720............34344

.0.....240......1584........9720.........54936.........299088..........1585800

.0....1344.....12960......118584.......1004184........8250912.........66210264

.0....6912.....98496.....1347192......17194680......214142760.......2611960344

.0...33792....715392....14644152.....282550680.....5344944120......99308573208

.0..159744...5038848...154472184....4513169016...129834259704....3679171151832

.0..737280..34712064..1594323000...70609114584..3091414865040..133712637011640

.0.3342336.235146240.16185567096.1087342615224.72488795124312.4788143315276472

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..287

Crossrefs

Row 1 is A167667(n-1).

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) -16*a(n-2)

k=3: a(n) = 12*a(n-1) -36*a(n-2)

k=4: a(n) = 18*a(n-1) -81*a(n-2) for n>3

k=5: a(n) = 30*a(n-1) -261*a(n-2) +540*a(n-3) -324*a(n-4)

k=6: a(n) = 50*a(n-1) -805*a(n-2) +4662*a(n-3) -12150*a(n-4) +14580*a(n-5) -6561*a(n-6)

k=7: [order 8]

Empirical for row n:

n=1: a(n) = 4*a(n-1) -4*a(n-2)

n=2: a(n) = 6*a(n-1) -9*a(n-2) for n>4

n=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>6

n=4: [order 6] for n>12

n=5: [order 14] for n>18

n=6: [order 18] for n>26

n=7: [order 54] for n>60