A268971 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

3, 9, 9, 24, 60, 27, 60, 240, 336, 81, 144, 912, 2016, 1728, 243, 336, 3312, 11664, 15552, 8448, 729, 768, 11664, 63792, 136080, 114048, 39936, 2187, 1728, 40176, 339480, 1125360, 1504656, 808704, 184320, 6561, 3840, 136080, 1770048, 9093528, 18852912

Offset: 1

Author

R. H. Hardin, Feb 16 2016

Keywords

• nonn
• tabl

Comments

Table starts

.....3........9.........24...........60............144..............336

.....9.......60........240..........912...........3312............11664

....27......336.......2016........11664..........63792...........339480

....81.....1728......15552.......136080........1125360..........9093528

...243.....8448.....114048......1504656.......18852912........231730344

...729....39936.....808704.....16061328......305242992.......5712070032

..2187...184320....5598720....167226768.....4823705520.....137497776840

..6561...835584...38071296...1709114256....74858700528....3251386055664

.19683..3735552..255301632..17218688400..1145496747312...75828095546544

.59049.16515072.1693052928.171498136464.17332683832944.1748970953035272

Examples

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

Links

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

Crossrefs

Column 1 is A000244.

Row 1 is A084858.

Formula

Empirical for column k:

k=1: a(n) = 3*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