login
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.
14
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 16 2016
STATUS
approved