A228796 T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.

1, 1, 2, 2, 2, 4, 3, 8, 5, 8, 5, 16, 36, 13, 16, 8, 42, 97, 156, 34, 32, 13, 98, 411, 586, 672, 89, 64, 21, 240, 1394, 3957, 3588, 2892, 233, 128, 34, 576, 5223, 19474, 37944, 22060, 12444, 610, 256, 55, 1394, 18708, 111966, 272952, 362511, 135768, 53544, 1597, 512

Offset

1,3

Comments

Table starts

...1....1......2.......3.........5...........8...........13.............21

...2....2......8......16........42..........98..........240............576

...4....5.....36......97.......411........1394.........5223..........18708

...8...13....156.....586......3957.......19474.......111966.........596273

..16...34....672....3588.....37944......272952......2404290.......19027372

..32...89...2892...22060....362511.....3835792.....51557716......607251543

..64..233..12444..135768...3459357....53992646...1104367784....19393508581

.128..610..53544..835776..33001836...760460212..23641626212...619684261316

.256.1597.230388.5145232.314810115.10712702564.505993241296.19806136078115

Links

R. H. Hardin, Table of n, a(n) for n = 1..1347

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) = 5*a(n-1) -3*a(n-2) for n>3

k=4: a(n) = 8*a(n-1) -12*a(n-2) +4*a(n-3) for n>4

k=5: a(n) = 13*a(n-1) -36*a(n-2) +29*a(n-3) -5*a(n-4) for n>6

k=6: a(n) = 21*a(n-1) -112*a(n-2) +217*a(n-3) -157*a(n-4) +36*a(n-5) for n>7

k=7: [order 7] for n>10

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2)

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

n=3: a(n) = a(n-1) +8*a(n-2) +6*a(n-3) -a(n-4) -a(n-5)

n=4: [order 8]

n=5: [order 13]

n=6: [order 21]

n=7: [order 34]

Example

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

Crossrefs

Column 1 is A000079(n-1)

Column 2 is A001519

Row 1 is A000045

Sequence in context: A240078 A344789 A228660 * A155837 A096445 A125915

Adjacent sequences: A228793 A228794 A228795 * A228797 A228798 A228799

Keyword

nonn,tabl

Author

R. H. Hardin Sep 04 2013

Status

approved