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

1,4

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

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

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

Adjacent sequences: A269008 A269009 A269010 * A269012 A269013 A269014

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 17 2016

Status

approved