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

Author

R. H. Hardin Feb 29 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A001519(n+1)

Column 3 is A199109(n-1)

Row 2 is A052940(n-1)

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