A269035 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 3, 0, 12, 24, 0, 36, 48, 120, 0, 96, 216, 348, 504, 0, 240, 672, 2166, 2136, 1944, 0, 576, 2208, 9528, 18384, 12228, 7128, 0, 1344, 6912, 44760, 115656, 146064, 67104, 25272, 0, 3072, 21408, 198816, 785124, 1326576, 1114848, 357756, 87480, 0, 6912, 65280

Offset: 1

Author

R. H. Hardin, Feb 18 2016

Keywords

• nonn
• tabl

Comments

Table starts

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

.0.....24.......48........216..........672...........2208............6912

.0....120......348.......2166.........9528..........44760..........198816

.0....504.....2136......18384.......115656.........785124.........4998648

.0...1944....12228.....146064......1326576.......13031664.......119790816

.0...7128....67104....1114848.....14710368......208867428......2783857776

.0..25272...357756....8277072....159397596.....3266423688.....63310818360

.0..87480..1867560...60218112...1698064656....50155587360...1416701634552

.0.297432..9593844..431354928..17853542544...759280601376..31304407671636

.0.997272.48665904.3052215072.185754411168.11364951702132.684763778434512

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..337

Crossrefs

Column 2 is A268633.

Row 1 is A167667(n-1).

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3

k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5

k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5

k=5: [order 12] for n>13

k=6: [order 18] for n>19

k=7: [order 38] for n>39

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)

n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8

n=4: [order 12] for n>14

n=5: [order 20] for n>22

n=6: [order 46] for n>48

n=7: [order 92] for n>94