login
A268886
T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
13
0, 1, 0, 2, 5, 0, 5, 14, 20, 0, 10, 54, 84, 71, 0, 20, 158, 501, 462, 235, 0, 38, 475, 2190, 4133, 2418, 744, 0, 71, 1340, 9996, 27130, 31956, 12252, 2285, 0, 130, 3740, 42362, 186732, 317966, 236960, 60666, 6865, 0, 235, 10204, 178400, 1187838, 3283890
OFFSET
1,4
COMMENTS
Table starts
.0.....1.......2.........5..........10............20..............38
.0.....5......14........54.........158...........475............1340
.0....20......84.......501........2190..........9996...........42362
.0....71.....462......4133.......27130........186732.........1187838
.0...235....2418.....31956......317966.......3283890........31427480
.0...744...12252....236960.....3596174......55491832.......800733668
.0..2285...60666...1706732....39670270.....911930096.....19876401224
.0..6865..295230..12034000...429588382...14681855846....483987898760
.0.20284.1417452..83485488..4585939726..232688402028..11611969197776
.0.59155.6732102.571836176.48401059362.3642322709900.275345016177616
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)
k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7
k=5: [order 8] for n>9
k=6: [order 10] for n>12
k=7: [order 14] for n>16
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6)
n=3: [order 9]
n=4: [order 16]
n=5: [order 26]
n=6: [order 42]
n=7: [order 68]
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0
..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..1..1. .0..1..0..0
..0..0..1..0. .1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..0..0
..1..0..1..0. .1..0..0..1. .1..1..0..1. .0..1..0..0. .1..0..0..0
CROSSREFS
Column 2 is A054444(n-1).
Row 1 is A001629.
Sequence in context: A196816 A058204 A242969 * A090625 A021403 A299623
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 15 2016
STATUS
approved