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

1,2

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

Links

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

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

Example

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

Crossrefs

Row 1 is A167667(n-1).

Sequence in context: A135687 A057374 A269035 * A058896 A186748 A222754

Adjacent sequences: A268901 A268902 A268903 * A268905 A268906 A268907

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 15 2016

Status

approved