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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000244.

Row 1 is A084858.

Sequence in context: A268809 A268628 A269052 * A267966 A263320 A226717

Adjacent sequences: A268968 A268969 A268970 * A268972 A268973 A268974

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 16 2016

Status

approved