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A269011
T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
13
0, 1, 0, 2, 4, 0, 5, 8, 15, 0, 10, 36, 46, 48, 0, 20, 88, 305, 224, 145, 0, 38, 272, 1078, 2136, 1066, 420, 0, 71, 696, 4948, 10976, 14240, 4952, 1183, 0, 130, 1900, 18210, 73568, 109058, 91048, 22654, 3264, 0, 235, 4856, 73277, 390064, 1049588, 1053432, 566656
OFFSET
1,4
COMMENTS
Table starts
.0.....1.......2.........5.........10...........20.............38
.0.....4.......8........36.........88..........272............696
.0....15......46.......305.......1078.........4948..........18210
.0....48.....224......2136......10976........73568.........390064
.0...145....1066.....14240.....109058......1049588........8134304
.0...420....4952.....91048....1053432.....14382480......164351184
.0..1183...22654....566656...10002542....192100836.....3258530608
.0..3264..102416...3456320...93733440...2516546784....63679868768
.0..8865..458674..20760192..869397882..32481770852..1230707111424
.0.23780.2038328.123186784.7996744280.414339126768.23573013881888
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -a(n-4)
k=3: a(n) = 10*a(n-1) -31*a(n-2) +24*a(n-3) +21*a(n-4) -18*a(n-5) -9*a(n-6)
k=4: a(n) = 12*a(n-1) -40*a(n-2) +8*a(n-3) +92*a(n-4) -32*a(n-5) -64*a(n-6) for n>7
k=5: [order 12]
k=6: [order 14]
k=7: [order 24] for n>25
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) -6*a(n-3) -9*a(n-4)
n=3: a(n) = 4*a(n-1) +8*a(n-2) -34*a(n-3) -16*a(n-4) +60*a(n-5) -25*a(n-6)
n=4: [order 8]
n=5: [order 14]
n=6: [order 20]
n=7: [order 32]
EXAMPLE
Some solutions for n=4 k=4
..1..1..0..0. .0..0..1..0. .1..0..1..1. .0..1..0..0. .0..0..0..0
..0..0..0..1. .0..0..1..0. .1..0..0..0. .0..0..1..0. .1..0..0..0
..0..0..0..0. .1..0..0..0. .1..0..0..1. .0..0..1..0. .0..1..0..0
..0..1..0..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..0..0
CROSSREFS
Column 2 is A093967.
Row 1 is A001629.
Sequence in context: A144810 A300753 A319275 * A274086 A255982 A256061
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 17 2016
STATUS
approved