A269011 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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

Author

R. H. Hardin, Feb 17 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..721

Crossrefs

Column 2 is A093967.

Row 1 is A001629.

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]