A208637 T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors

1, 2, 2, 4, 5, 4, 8, 11, 13, 8, 16, 23, 32, 34, 16, 32, 47, 71, 95, 89, 32, 64, 95, 150, 225, 284, 233, 64, 128, 191, 309, 494, 722, 851, 610, 128, 256, 383, 628, 1042, 1652, 2331, 2552, 1597, 256, 512, 767, 1267, 2149, 3577, 5572, 7548, 7655, 4181, 512, 1024, 1535

Offset

1,2

Comments

Table starts

...1....2....4.....8....16.....32.....64....128.....256.....512....1024

...2....5...11....23....47.....95....191....383.....767....1535....3071

...4...13...32....71...150....309....628...1267....2546....5105...10224

...8...34...95...225...494...1042...2149...4375....8840...17784...35687

..16...89..284...722..1652...3577...7504..15448...31440...63543..127884

..32..233..851..2331..5572..12404..26508..55260..113427..230559..465773

..64..610.2552..7548.18888..43284..94320.199299..412962..844943.1714680

.128.1597.7655.24476.64216.151656.337227.722733.1512764.3117620.6359210

Links

R. H. Hardin, Table of n, a(n) for n = 1..1193

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 3*a(n-1) -a(n-2)

k=3: a(n) = 4*a(n-1) -3*a(n-2)

k=4: a(n) = 5*a(n-1) -6*a(n-2) +a(n-3)

k=5: a(n) = 6*a(n-1) -10*a(n-2) +4*a(n-3)

k=6: a(n) = 7*a(n-1) -15*a(n-2) +10*a(n-3) -a(n-4)

k=7: a(n) = 8*a(n-1) -21*a(n-2) +20*a(n-3) -5*a(n-4)

Empirical for row n:

n=1: a(k)=2*a(k-1)

n=2: a(k)=3*a(k-1)-2*a(k-2)

n=3: a(k)=4*a(k-1)-5*a(k-2)+2*a(k-3)

n=4: a(k)=5*a(k-1)-9*a(k-2)+7*a(k-3)-2*a(k-4) for k>5

n=5: a(k)=6*a(k-1)-14*a(k-2)+16*a(k-3)-9*a(k-4)+2*a(k-5) for k>7

n=6: a(k)=7*a(k-1)-20*a(k-2)+30*a(k-3)-25*a(k-4)+11*a(k-5)-2*a(k-6) for k>9

n=7: a(k)=8*a(k-1)-27*a(k-2)+50*a(k-3)-55*a(k-4)+36*a(k-5)-13*a(k-6)+2*a(k-7) for k>11

Example

Some solutions for n=4 k=3
..0..0..0....0..0..1....0..1..1....0..0..1....0..0..1....0..1..0....0..1..0
..1..1..0....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1
..0..1..1....0..1..0....0..1..0....0..1..0....1..0..0....0..1..0....1..0..1
..0..0..1....1..0..1....0..1..0....0..1..0....1..1..0....1..0..1....1..0..0

Crossrefs

Column 2 is A001519(n+1)

Column 3 is A199109(n-1)

Row 2 is A052940(n-1)

Sequence in context: A286101 A072454 A115216 * A341867 A252938 A229402

Adjacent sequences: A208634 A208635 A208636 * A208638 A208639 A208640

Keyword

nonn,tabl

Author

R. H. Hardin Feb 29 2012

Status

approved