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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 2 is A268633.

Row 1 is A167667(n-1).

Sequence in context: A269880 A135687 A057374 * A268904 A058896 A186748

Adjacent sequences: A269032 A269033 A269034 * A269036 A269037 A269038

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 18 2016

Status

approved